Publications and Preprints

• List by subjects
• Chronological list
• Conference proceedings and similar
• My publications on Arxiv, MathScinet and Zentralblatt
• Other material

List by subjects

• Parallel spinors and special holonomy

  • Dominant energy condition and spinors on Lorentzian manifolds (with J. Glöckle), Perspectives in Scalar Curvature, Volume II, Edited By: M. Gromov and H. B. Lawson, 2023, doi: 10.1142/12644
  • Construction of initial data sets for Lorentzian manifolds with lightlike parallel spinors (with K. Kröncke and O. Müller), Commun. Math. Phys. 387, 77-109 (2021), doi: 10.1007/s00220-021-04172-1,
  • Holonomy rigidity for Ricci-flat metrics (with K. Kröncke, H. Weiss, and F. Witt), Math. Z. 291, 303-311 (2019), doi: 10.1007/s00209-018-2084-3

• Conformal spin geometry and Yamabe problem

  • The S¹-equivariant Yamabe invariant of 3-manifolds, (with F. Madani and M. Pilca), Int. Math. Res. Not. (IMRN), 2017 (20), 6310-6328 (2017), doi: 10.1093/imrn/rnw194
  • Relations between threshold constants for Yamabe type bordism invariants (with N. Große), J. Geom. Anal. 26, 2842-2882 (2016)
  • Positive mass theorem for some asymptotically hyperbolic manifolds (with N. Große), Abh. Math. Sem. Hamburg 87, 165-180 (2017)
    
  • Low-dimensional surgery and the Yamabe invariant (with M. Dahl, and E. Humbert), J. Math. Soc. Japan 67, 159-182 (2015)
  • Square-integrability of solutions of the Yamabe equation, (with M. Dahl, and E. Humbert), Commun. Anal. Geom. 21, 891-916 (2013)
  • The conformal Yamabe invariant of product manifolds (with M. Dahl, and E. Humbert) Proc. AMS 141, 295-307 (2013)
  • Mass endomorphism, surgery and perturbations (with M. Dahl, A. Hermann, and E. Humbert), Ann. Inst. Fourier 64, 467-487 (2014)
  • Harmonic spinors and local deformations of the metric (with M. Dahl and E. Humbert), Math. Res. Lett. 18, 927-936 (2011)
  • Smooth Yamabe invariant and surgery (with M. Dahl and E. Humbert), J. Diff. Geom. 94, 1-58 (2013)
  • Surgery and the spinorial τ-invariant (with M. Dahl and E. Humbert) Comm. Part. Diff. Eq. 34, 1147-1179 (2009)
  • The supremum of first eigenvalues of conformally covariant operators in a conformal class (with P. Jammes), in Variational Problems in Differential Geometry, Proceedings of a Conference in Leeds on the occasion of J. Woods 60th birthday, Leeds 2009, London Mathematical Society Lecture Notes Series 394, 1-23 (2011)
  • The spinorial τ-invariant and 0-dimensional surgery (with E. Humbert), J. reine angew. Math. 624, 27-50 (2008)
  • Surgery and harmonic spinors (with M. Dahl and E. Humbert), Adv. Math. 220 no. 2, 523-539 (2009)
  • An obstruction for the mean curvature of a conformal immersion Sⁿ→ Rⁿ⁺¹ (with E. Humbert and M. O. Ahmedou), Proc. AMS 135, 489-493 (2007)
  • The second Yamabe invariant (with E. Humbert), J. Funct. Anal. 235 no. 2, 377-412 (2006)
  • The first conformal Dirac eigenvalue on 2-dimensional tori (with E. Humbert), J. Geom. Phys. 56, 623-642 (2006)
  • Mass endomorphism and spinorial Yamabe type problems on conformally flat manifolds (with E. Humbert and B. Morel) Comm. Anal. Geom. 14 no. 1, 163-182 (2006)
  • Habilitationsschrift: A Variational Problem in Conformal Spin Geometry, Universität Hamburg, 16.5.2003. (Postscript version)
  • The smallest Dirac eigenvalue in a spin-conformal class and cmc-immersions, Comm. Anal. Geom. 17, 429-479 (2009)
  • A spinorial analogue of Aubin's inequality (with J.F. Grosjean, E. Humbert and B. Morel), Math. Z. 260, 127-151 (2008)
  • Positive mass theorem for the Yamabe problem on spin manifolds (with E. Humbert) GAFA 15, 567-576 (2005)
  • A spin-conformal lower bound of the first positive Dirac eigenvalue, Differential Geometry and its applications 18 no. 1, 21-32 (2003)

• Pseudodifferential operators on Lie manifolds and related subjects

  • A regularity result for the bound states of N-body Schrödinger operators: Blow-ups and Lie manifolds (with V. Nistor and J. Mougel), Lett. Math. Phys. 113, 26-53 (2023)
  • A comparison of the Georgescu and Vasy spaces associated to the N-body problems and applications (with V. Nistor and J. Mougel), Annales Henri Poincaré 23, 1141-1203 (2022)
  • Regularity for eigenfunctions of Schrödinger operators (with V. Nistor and C. Carvalho), Lett. Math. Phys. 101, 49-84 (2012)
  • Weighted Sobolev spaces and regularity for polyhedral domains (with V. Nistor), Comput. Methods Appl. Mech. Engrg. 196, 3650-3659 (2007).
  • Sobolev spaces on Lie manifolds and regularity for polyhedral domains (with A. Ionescu and V. Nistor). Doc. Math. 11, 161-206 (2006)
  • Overview article: Algebras of Pseudodifferential Operators on complete manifolds (with R. Lauter and V. Nistor) Electronic Research Announcements of the AMS 9 80-87 (2003).
  • Pseudodifferential operators on manifolds with a Lie structure at infinity (with R. Lauter and V. Nistor), Ann. of Math. 165, 717-747 (2007).
  • Complex powers and non-compact manifolds (with R. Lauter, V. Nistor and A. Vasy), Comm. Part. Diff. Eq. 29, no. 5/6 671-705 (2004)
  • On the geometry of Riemannian manifolds with a Lie structure at infinity (with R. Lauter and V. Nistor), Int. J. Math. and Math. Sciences 2004:4 no. 4, 161-193 (2004)

• Spinor flow

  • The spinorial energy functional on surfaces (with H. Weiss, and F. Witt), Math. Z. 282, 177-202 (2016), doi: 10.1007/s00209-015-1537-1.
  • A spinorial energy functional: critical points and gradient flow (with H. Weiss, and F. Witt), Math. Ann. 365, 1559-1602 (2016), doi: 10.1007/s00208-015-1315-8.

• Dirac-harmonic maps

  • Are all Dirac-harmonic maps uncoupled?, Preprint 2022
  • Some examples of Dirac-harmonic maps (with N. Ginoux), Lett. Math. Phys. 109, 1205-1218 (2019), doi: 10.1007/s11005-018-1134-4
  • Dirac-harmonic maps from index theory (with N. Ginoux), Calc. Var. 47, 739-762, (2013).

• Various topics

  • Analysis and boundary value problems on singular domains: an approach via bounded geometry (with V. Nistor and N. Große), Comptes Rendus Mathématique 357, 487-493 (2019), doi: 10.1016/j.crma.2019.04.009,
  • The strong Legendre condition and the well-posedness of mixed Robin problems on manifolds with bounded geometry, (with V. Nistor and N. Große), Rev. Roumaine Math. Pures Appl. 64, 85-111 (2019), direct link
  • Well-posedness of the Laplacian on manifolds with boundary and bounded geometry (with V. Nistor and N. Große) Math. Nachr. 292 no. 7, 1213-1237 (2019), doi: 10.1002/mana.201700408
  • The Cauchy problem for metrics with parallel spinors (with A. Moroianu and S. Moroianu), Commun. Math. Phys. 320, 173-198 (2013), doi: 10.1007/s00220-013-1714-1.

• Spectral theory for Dirac and Laplace operators

  • L^p-spectrum of the Dirac operator on products with hyperbolic spaces (with N. Große), Calc. Var. Partial Differential Equations 55 (2016), 55:127.
  • Manifolds with small Dirac eigenvalues are nilmanifolds (with C. Sprouse), Ann. Glob. Anal. Geom. 31, 409-425 (2007)
  • A spin-conformal lower bound of the first positive Dirac eigenvalue, Differential Geometry and its applications 18 no.1, 21-32 (2003)
  • Dirac eigenvalue estimates on surfaces (with C. Bär), Math. Z. 240, 423-449 (2002)
  • Dirac eigenvalue estimates on 2-tori, J. Geom. Phys. 51 no. 3, 372-386 (2004)
    (This is a shorter version of Spectral estimates on 2-tori.)
  • Dirac eigenvalues and total scalar curvature (mit C. Bär), J. Geom. Phys. 33, 229-234 (2000)
  • The Willmore Conjecture for immersed tori with small curvature integral, Manuscripta Math. 101 no. 1, 1-22 (2000)
  • A comparison of the eigenvalues of the Dirac and Laplace operator on the two-dimensional torus, Manuscripta Math. 100, no. 2, 231-258 (1999) (mit T. Friedrich und I. Agricola)
  • The Dirac operator on Collapsing S¹-bundles Sém. Th. Spec. Géom Inst. Fourier Grenoble 16 33-42 (1998)
  • Spin-Strukturen und das Spektrum des Dirac-Operators, Dissertation, Mai 1998 (.pdf,.ps,.ps.gz)
  • The Dirac Operator on Nilmanifolds and Collapsing Circle Bundles (mit C. Bär) Ann. Glob. Anal. Geom. 16, no. 3, 221-253 (1998)

• Minimal geodesics

  • A quadratic lower bound for the number of minimal geodesics, (with Clara Löh), Preprint 2023
  • Minimal Geodesics and Nilpotent Fundamental Groups Geometriae dedicata 67, 129-148 (1997)

Chronological list

• A quadratic lower bound for the number of minimal geodesics, (with Clara Löh), Preprint 2023
• Are all Dirac-harmonic maps uncoupled?, Preprint 2022
• Dominant energy condition and spinors on Lorentzian manifolds (with J. Glöckle), Preprint 2021
• A regularity result for the bound states of N-body Schrödinger operators: Blow-ups and Lie manifolds (with V. Nistor and J. Mougel), Lett. Math. Phys. 113, 26-53 (2023)
• A comparison of the Georgescu and Vasy spaces associated to the N-body problems and applications (with V. Nistor and J. Mougel), Annales Henri Poincaré 23, 1141-1203 (2022)
• Construction of initial data sets for Lorentzian manifolds with lightlike parallel spinors (with K. Kröncke and O. Müller), Commun. Math. Phys. 387, 77-109 (2021), doi: 10.1007/s00220-021-04172-1, Direct publisher's link (open access): https://rdcu.be/crPr1
• Analysis and boundary value problems on singular domains: an approach via bounded geometry (with V. Nistor and N. Große), Comptes Rendus Mathématique 357, 487-493 (2019), doi: 10.1016/j.crma.2019.04.009,
• Some examples of Dirac-harmonic maps (with N. Ginoux), Lett. Math. Phys. 109, 1205-1218 (2019), doi: 10.1007/s11005-018-1134-4
• The strong Legendre condition and the well-posedness of mixed Robin problems on manifolds with bounded geometry (with V. Nistor and N. Große), Rev. Roumaine Math. Pures Appl. 64, 85-111 (2019), direct link
• Well-posedness of the Laplacian on manifolds with boundary and bounded geometry (with V. Nistor and N. Große) Math. Nachr. 292 no. 7, 1213-1237 (2019), doi: 10.1002/mana.201700408
• Holonomy rigidity for Ricci-flat metrics (with K. Kröncke, H. Weiss, and F. Witt), Math. Z. 291, 303-311 (2019), doi: 10.1007/s00209-018-2084-3
• The S¹-equivariant Yamabe invariant of 3-manifolds (with F. Madani and M. Pilca), Int. Math. Res. Not. (IMRN) 2017 (20), 6310-6328 (2017), doi: 10.1093/imrn/rnw194
• Positive mass theorem for some asymptotically hyperbolic manifolds (with N. Große), Abh. Math. Sem. Hamburg 87, 165-180 (2017)
  
• Relations between threshold constants for Yamabe type bordism invariants (with N. Große), J. Geom. Anal. 26, 2842-2882 (2016)
• L^p-spectrum of the Dirac operator on products with hyperbolic spaces (with N. Große), Calc. Var. Partial Differential Equations 55 (2016), 55:127.
• The spinorial energy functional on surfaces (with H. Weiss, and F. Witt), Math. Z. 282, 177-202 (2016), doi: 10.1007/s00209-015-1537-1
• A spinorial energy functional: critical points and gradient flow (with H. Weiss, and F. Witt), Math. Ann. 365, 1559-1602 (2016), doi: 10.1007/s00208-015-1315-8
• Low-dimensional surgery and the Yamabe invariant (with M. Dahl, and E. Humbert) J. Math. Soc. Japan 67, 159-182 (2015)
• Regularity for eigenfunctions of Schrödinger type operators. A research report about joint work with V. Nistor and C. Carvalho, Math. Forsch. Oberwolfach Report 56/2011 (2011), 3223-3225, doi: 10.4171/OWR/2011/56
• The Cauchy problem for metrics with parallel spinors (with A. Moroianu and S. Moroianu), Commun. Math. Phys. 320 173-198 (2013), doi: 10.1007/s00220-013-1714-1.
• Square-integrability of solutions of the Yamabe equation (with M. Dahl, and E. Humbert), Commun. Anal. Geom. 21, 891-916 (2013)
• Dirac-harmonic maps from index theory (with N. Ginoux), Calc. Var. 47, 739-762, (2013).
• The conformal Yamabe invariant of product manifolds (with M. Dahl, and E. Humbert), Proc. AMS 141, 295-307 (2013)
• Regularity for eigenfunctions of Schrödinger operators (with V. Nistor and C. Carvalho), Lett. Math. Phys. 101, 49-84 (2012)
• Mass endomorphism, surgery and perturbations (with M. Dahl, A. Hermann, and E. Humbert) Ann. Inst. Fourier 64, 467-487 (2014)
• Harmonic spinors and local deformations of the metric (with M. Dahl and E. Humbert), Math. Res. Lett. 18, 927-936 (2011)
• Smooth Yamabe invariant and surgery (with M. Dahl and E. Humbert), J. Diff. Geom. 94, 1-58 (2013)
• Surgery and the spinorial τ-invariant (with M. Dahl and E. Humbert) Comm. Part. Diff. Eq. 34, 1147-1179 (2009)
• The supremum of first eigenvalues of conformally covariant operators in a conformal class (with P. Jammes), in Variational Problems in Differential Geometry, Proceedings of a Conference in Leeds on the occasion of J. Woods 60th birthday, Leeds 2009, London Mathematical Society Lecture Notes Series 394, 1-23 (2011)
• The spinorial τ-invariant and 0-dimensional surgery (with E. Humbert), J. reine angew. Math. 624, 27-50 (2008)
• Surgery and harmonic spinors (with M. Dahl and E. Humbert), Adv. Math. 220 no. 2, 523-539 (2009)
• The first eigenvalue of the Dirac operator in a conformal class (with E. Humbert), Int. J. Geom. Methods Mod. Phys. 3 (2006), no. 5-6, 833-844.
• Weighted Sobolev spaces and regularity for polyhedral domains (with V. Nistor), Comput. Methods Appl. Mech. Engrg. 196, 3650-3659 (2007)
• An obstruction for the mean curvature of a conformal immersion Sⁿ→ Rⁿ⁺¹ (with E. Humbert and M. O. Ahmedou), Proc. AMS 135, 489-493 (2007)
• The second Yamabe invariant (with E. Humbert), J. Funct. Anal. 235 no. 2, 377-412 (2006)
• The first conformal Dirac eigenvalue on 2-dimensional tori (with E. Humbert), J. Geom. Phys. 56, 623-642 (2006)
• Manifolds with small Dirac eigenvalues are nilmanifolds (with C. Sprouse), Ann. Glob. Anal. Geom. 31, 409-425 (2007)
• Sobolev spaces on Lie manifolds and regularity for polyhedral domains (with A. Ionescu and V. Nistor). Doc. Math. 11 161-206 (2006)
• Mass endomorphism and spinorial Yamabe type problems on conformally flat manifolds (with E. Humbert and B. Morel) Comm. Anal. Geom. 14 no. 1, 163-182 (2006)
• A spinorial analogue of Aubin's inequality (with J.F. Grosjean, E. Humbert and B. Morel), Math. Z. 260, 127-151 (2008)
• Algebras of Pseudodifferential Operators on complete manifolds (with R. Lauter and V. Nistor) Electronic Research Announcements of the AMS 9, 80-87 (2003)
• Habilitationsschrift: A Variational Problem in Conformal Spin Geometry, Universität Hamburg, 16.5.2003. (Postscript version)
• The smallest Dirac eigenvalue in a spin-conformal class and cmc-immersions, Comm. Anal. Geom. 17, 429-479 (2009)
• Positive mass theorem for the Yamabe problem on spin manifolds (with E. Humbert) GAFA 15, 567-576 (2005)
• Pseudodifferential operators on manifolds with a Lie structure at infinity (with R. Lauter and V. Nistor), Ann. of Math. 165, 717-747 (2007)
• Complex powers and non-compact manifolds (with R. Lauter, V. Nistor and A. Vasy), Comm. Part. Diff. Eq. 29, no. 5/6 671-705 (2004)
• On the geometry of Riemannian manifolds with a Lie structure at infinity (with R. Lauter and V. Nistor), Int. J. Math. and Math. Sciences 2004:4, 161--193 (2004)
• A spin-conformal lower bound of the first positive Dirac eigenvalue, Differential Geometry and its applications 18 no.1, 21-32 (2003)
• Dirac eigenvalue estimates on surfaces (mit C. Bär), Math. Z. 240, 423-449 (2002)
• Dirac eigenvalue estimates on 2-tori, J. Geom. Phys. 51 no.3, 372-386 (2004)
  (This is a shorter version of Spectral estimates on 2-tori.)
• Dirac eigenvalues and total scalar curvature (mit C. Bär), J. Geom. Phys. 33, 229-234 (2000)
• The Willmore Conjecture for immersed tori with small curvature integral, Manuscripta Math. 101, no. 1, 1-22 (2000)
• A comparison of the eigenvalues of the Dirac and Laplace operator on the two-dimensional torus, Manuscripta Math. 100, no. 2, 231-258 (1999) (mit T. Friedrich und I. Agricola)
• The Dirac operator on Collapsing S¹-bundles Sém. Th. Spec. Géom Inst. Fourier Grenoble 16, 33-42 (1998)
• Spin-Strukturen und das Spektrum des Dirac-Operators, Dissertation, Mai 1998 (.pdf, .ps,.ps.gz)
• The Dirac Operator on Nilmanifolds and Collapsing Circle Bundles (mit C. Bär) Ann. Glob. Anal. Geom. 16, no. 3, 221-253 (1998)
• Minimal Geodesics and Nilpotent Fundamental Groups Geometriae dedicata 67, 129-148 (1997)

Conference Proceedings/Vorträge

• Lower bounds for the Yamabe invariant. Research report about joint work with M. Dahl and E. Humbert, Math. Forsch. Oberwolfach Report 25/2012 (2012), 1503-1506, doi: 10.4171/OWR/2012/25
• Regularity for eigenfunctions of Schrödinger type operators . Research report about joint work with V. Nistor and C. Carvalho, Math. Forsch. Oberwolfach Report 56/2011 (2011), 3223-3225, doi: 10.4171/OWR/2011/56
• A surgery formula for the smooth Yamabe invariant. Research report about joint work with M. Dahl and E. Humbert, Math. Forsch. Oberwolfach Report 41/2007 (2007), 2413-2417
• La dimension du noyau de l'opérateur de Dirac (with M. Dahl and E. Humbert), Journées Élie Cartan 2006, 2007, 2008, Proceedings, D. Barlet et al. (ed.),
  
• Metrics with few harmonic spinors (with M. Dahl and E. Humbert), Math. Forsch. Oberwolfach Report No. 53 (2006), 3144-3146
• The first eigenvalue of the Dirac operator in a conformal class (with E. Humbert), Int. J. Geom. Methods Mod. Phys. 3 (2006), no. 5-6, 833-844.
• Ambient Dirac eigenvalue estimates and the Willmore functional in: "Dirac operators: Yesterday and Today". Proceedings of the Summer School and Workshop, at CAMS-AUB-Lebanon, 2001. International Press 2005. Editors: Bourguignon, Branson, Chamseddine, Hijazi, Stanton, 221-228.
• The Einstein-Hilbert Action as a Spectral Action, Vortrag auf der Arbeitstagung "Das Standardmodell der Elementarteilchenphysik unter mathematisch-geometrischem Aspekt", Hesselberg, 14.-19. März 1999, mit Christian Bär.

All my publications on ...

• the ArXiv or here
• the AMS-MathSciNet (including reviews)
• the Zentralblatt (including reviews)

Other material

Lecture Notes/Vorlesungsskripte

• Analysis auf Mannigfaltigkeiten und Indextheorie, WS 2002/2003.

Diplom- und Doktorarbeit

• In meiner Dissertation untersuche ich das Spektrum des Dirac-Operators, insbesondere die Abhängigkeit des Spektrums von der Spin-Struktur. Die Dissertation wurde von Prof. C. Bär betreut.
  Die Doktorarbeit Spin-Strukturen und das Spektrum des Dirac-Operators (ISBN 3-8265-4282-7) wurde im Mai 1998 abgegeben und wurde beim Shaker Verlag veröffentlicht. Elektronisch kann die Doktorarbeit hier runtergeladen werden.
  Eine etwas anschaulichere Beschreibung der Dissertation kann hier runtergeladen werden.
• In meiner Diplomarbeit untersuchte ich Existenzaussagen für minimale Geodätische auf Mannigfaltigkeiten mit nilpotenter Fundamentalgruppe. Nähere Informationen erhält man im oben gelinkten Preprint "Minimal geodesics and nilpotent fundamental groups". Die Diplomarbeit wurde von Prof. V. Bangert betreut.
  Elektronisch kann die Diplomarbeit hier auf meinem Webserver oder hier auf dem Publikationsserver der Universität Regensburg heruntergeladen werden.