Ruprecht-Karls-Universität Heidelberg Institut für Angewandte Mathematik  Prof. Dr. Claus Gerhardt

List of publications (pdf)

My papers on arXiv

Mathematical Genealogy (pdf)

Extending the solutions and the equations of quantum gravity past the big bang singularity (pdf)
Dec. 17, 2024
doi:10.13140/RG.2.2.24262.38720

The quantization of gravity, 2nd edition: Front Matter (pdf)
Fundamental Theories of Physics, vol 194, 276 pages, Springer, Cham, November 2024
doi:10.1007/978-3-031-67922-3

The quantization of gravity: The quantization of the full Einstein equations (pdf)
Symmetry 15, No. 8, 1599 (2023)
doi:10.3390/sym15081599

A unified quantization of gravity and other fundamental forces of nature implies a big bang on the quantum level (pdf)
Jan. 25, 2023
doi:10.13140/RG.2.2.11042.71361

A unified quantization of gravity and other fundamental forces of nature (pdf)
Universe 8, No. 8, 404 (2022)
doi:10.3390/universe8080404

The quantization of gravity: Quantization of the Hamilton equations (pdf)
Universe 7, No. 4, 91 (2021)
doi:10.3390/universe7040091

CMC foliations of open spacetimes asymptotic to open Robertson-Walker spacetimes (pdf)
Feb. 2, 2019, To be published in Pure and Applied Mathematics Quarterly

Applications of canonical quantum gravity to cosmology (pdf)
Symmetry 11, No. 8, 1005 (2019)
doi:10.3390/sym11081005

The quantization of gravity (pdf)
Adv. Theor. Math. Phys. 22, 709 - 757 (2018)

Trace class estimates and applications (pdf)
Nov. 2, 2017

A partition function for Schwarzschild-AdS and Kerr-AdS black holes and for quantized globally hyperbolic spacetimes with a negative cosmological constant (pdf)
Oct. 1, 2017

The quantization of a Kerr-AdS black hole (pdf)
Aug. 5, 2017

The quantum development of an asymptotically Euclidean Cauchy hypersurface (pdf)
Jan. 20, 2017

The quantization of a black hole (pdf)
Aug. 29, 2016

Deriving a complete set of eigendistributions for a gravitational wave equation describing the quantized interaction of gravity with a Yang-Mills field in case the Cauchy hypersurface is non-compact (pdf)
May 11, 2016

A unified field theory II: Gravity interacting with a Yang-Mills and Higgs field (pdf)
Feb. 14, 2016

Pinching estimates for dual flows in hyperbolic and de Sitter space (pdf)
iPad version
Okt. 13, 2015

A unified field theory I: The quantization of gravity (pdf)
Jan. 15, 2016
The paper has been published in ATMP (2018) under the title "The quantization of gravity".
Adv. Theor. Math. Phys. 22, 709 - 757 (2018)

Curvature flows in the sphere (pdf)
iPad version
Aug. 7, 2013
J. Differential Geom. 100, 301 - 347 (2015)
Permament link

A unified quantum theory II: gravity interacting with Yang-Mills and spinor fields (pdf)
iPad version
Jan. 25, 2013

A unified quantum theory I: gravity interacting with a Yang-Mills field (pdf)
iPad version
July 3, 2012
Adv. Theor. Math. Phys. 18, 1043 - 1062 (2014)
doi:10.4310/ATMP.2014.v18.n5.a2

The quantization of gravity in globally hyperbolic spacetimes (pdf)
iPad version
May 7, 2012
Adv. Theor. Math. Phys. 17, 1357 - 1391 (2013)
doi:10.4310/ATMP.2013.v17.n6.a5
also available from arXiv:1205.1427

Non-scale-invariant inverse curvature flows in Euclidean space (pdf)
iPad version
May 31, 2011
Cal. Var. PDE 14, 471 - 489 (2014)
doi:10.1007/s00526-012-0589-x

Inverse curvature flows in hyperbolic space (pdf)
iPad version
Journal Diff. Geom. 89, 487 - 527 (2011)
also available from arXiv:1101.2578

Combining gravity with the forces of the Standard Model on a cosmological scale (pdf)
iPad version
Class. Quantum Grav. 27 (2010) 155008
doi:10.1088/0264-9381/27/15/155008
also available from arXiv:1003.4246

An energy gap for Yang-Mills connections (pdf)
iPad version
Commun. Math. Phys. 298, 515 - 522 (2010)
doi:10.1007/s00220-010-1073-0
also available from arXiv:0908.0767

Quantum cosmological Friedman models with a Yang-Mills field and positive energy levels (pdf)
Class. Quantum Grav. 27 (2010) 035007
doi:10.1088/0264-9381/27/3/035007
also available from arXiv:0907.5403

Quantum cosmological Friedman models with a massive Yang-Mills field (pdf)
Class. Quantum Grav. 26 (2009) 135013
doi:10.1088/0264-9381/26/13/135013
also available from arXiv:0903.1370

Curvature flows and CMC hypersurfaces (pdf)
Handbook of Geometric Analysis (Vol. III) (Lizhen Ji and Peter Li and Richard Schoen and Leon Simon, eds.), Advanced Lectures in Mathematics, vol. 14, Higher Education Press and International Press, Beijing-Boston, 2010, pp. 77 - 127
also available from arXiv:0806.1968

Quantum cosmological Friedman models with an initial singularity (pdf)
Class. Quantum Grav. 26 (2009) 015001 (29pp)
doi:10.1088/0264-9381/26/1/015001
also available from arXiv:0806.1769

A general existence proof for non-linear elliptic equations in semi-Riemannian spaces (pdf)
Am. J. Math. 131, 1569 - 1588 (2009)
also available from arXiv:0709.3123

Curvature estimates for Weingarten hypersurfaces in Riemannian manifolds (pdf)
Adv. Calc. Variations 1, 123 - 132 (2008)
also available from arXiv:0704.1021

Curvature flows in semi-Riemannian manifolds (pdf)
Surveys in Differential Geometry XII, 113 - 165 (2008)
also available from arXiv:0704.0236

Minkowski type problems for convex hypersurfaces in hyperbolic space (pdf)
February 27, 2006
also available from math.DG/0602597
bibtex data

Minkowski type problems for convex hypersurfaces in the sphere (pdf)
Pure and Applied Mathematics Quarterly 3, 417 - 449 (2007) (Leon Simon special issue, part I)
also available from math.DG/0509217
bibtex data

Branes, moduli spaces and smooth transition from big crunch to big bang (pdf)
Adv. Theor. Math. Phys. 10, 283 - 315 (2006)
also available from hep-th/0409123
bibtex data

On the CMC foliation of future ends of a spacetime (pdf)
Pacific J. Math. 226, 297 - 308 (2006)
also available from math.DG/0408197
bibtex data

The inverse mean curvature flow in Robertson-Walker spaces and its application to cosmology (pdf)
Methods Appl. Analysis 13, 19 - 28 (2006)
also available from gr-qc/0404112
bibtex data

Transition from big crunch to big bang in brane cosmology (pdf)
Adv. Theor. Math. Phys. 8, 319 - 343 (2004)
also available from gr-qc/0404061
bibtex data

The inverse mean curvature flow in ARW spaces - transition from big crunch to big bang (pdf)
also available from math.DG/0403485
bibtex data

The inverse mean curvature flow in cosmological spacetimes (pdf)
Adv. Theor. Math. Phys. 12, 1183 - 1207 (2008)
also available from math.DG/0403097
bibtex data

The mass of a Lorentzian manifold (pdf)
Adv. Theor. Math. Phys. 10, 33 - 48 (2006)
also available from math.DG/0403002
bibtex data

Estimates for the volume of a Lorentzian manifold (pdf)
Gen. Relativity Gravitation 35, 201 - 207 (2003)
The e-print contains additional results.
html version
also available from math.DG/0207049
bibtex data

Closed Weingarten hypersurfaces in semi-riemannian manifolds (pdf)
November 6, 2001
also available from math.DG/0207053
bibtex data

Hypersurfaces of prescribed scalar curvature in Lorentzian manifolds (pdf)
J. reine angew. Math. 554, 157 - 199 (2003)
also available from math.DG/0207054
bibtex data

Hypersurfaces of prescribed curvature in Lorentzian manifolds (pdf)
Indiana Univ. Math. J. 49, 1125 - 1152 (2000)
also available from math.DG/0409457
bibtex data

Hypersurfaces of prescribed mean curvature in Lorentzian manifolds (pdf)
Math. Z.  235, 83 - 97 (2000)
also available from math.DG/0409465
bibtex data

On the foliation of space-time by constant mean curvature hypersurfaces (pdf)
March 21, 1999
also available from math.DG/0304423
bibtex data

Closed hypersurfaces of prescribed mean curvature in locally conformally flat Riemannian manifolds (pdf)
Journal Diff. Geom. 48, 587 - 613 (1998)
also available from math.DG/0409467
bibtex data

Erratum: Hypersurfaces of prescribed Weingarten curvature (pdf)
Math. Z.  233, 829 - 830 (2000)
bibtex data

Hypersurfaces of prescribed Weingarten curvature (pdf)
Math. Z.  224, 167 - 194 (1997)
bibtex data

Closed Weingarten hypersurfaces in space forms (pdf)
Geometric Analysis and the Calculus of Variations (J. Jost, ed.),  International Press, Boston, pp. 71 - 98 (1996)
bibtex data

Closed Weingarten hypersurfaces in Riemannian manifolds (pdf)
Journal Diff. Geom. 43, 612 - 641 (1996)
bibtex data

Flow of nonconvex hypersurfaces into spheres (pdf)
Journal Diff. Geom. 32, 299 - 314 (1990)

Global $C^{1,1}$-regularity for solutions to quasi-linear variational inequalities (pdf)
Arch. Rat. Mech. Analysis 89, 83 - 92 (1985)

H-surfaces in Lorentzian manifolds (pdf)
Commun. Math. Phys. 89, 523 - 553 (1983)
bibtex data

Evolutionary surfaces of prescribed mean curvature (pdf)
J. Diff. Eq. 36, 139 - 172 (1980)

Boundary value problems for surfaces of prescribed mean curvature (pdf)
J. Math. Pure Appl. 58, 75 - 109 (1979)

Global regularity of the solutions to the capillarity problem (pdf)
Ann. Sc. Norm. Sup. Pisa, Ser. IV, 3, 157 - 175 (1976)

On the existence and uniqueness of a warpening function in the elastic-plastic torsion of a cylindrical bar with multiply connected cross-section (pdf)
Joint IUTAM/IMU Symposium in Applications of functional analysis to problems of mechanics , Lecture Notes in Mathematics, vol. 503, 328 - 342, Springer Verlag, Berlin-Heidelberg-New York, 1976

Regularity of solutions of nonlinear variational inequalities with a gradient bound as constraint (pdf)
Arch. Rat. Mech. Analysis 58, 309 - 315 (1975)

Existence, regularity, and boundary behaviour of generalized surfaces of prescribed mean curvature (pdf)
Math. Z. 139, 173 - 198 (1974)
bibtex data

Existence and regularity of capillary surfaces (pdf)
Boll. Un. Mat. Ital. 10, 317 - 335 (1974)

Regularity of solutions of nonlinear variational inequalities (pdf)
Arch. Rat. Mech. Analysis 52, 389 - 393 (1973)

Hypersurfaces of prescribed mean curvature over obstacles (pdf)
Math. Z. 133, 169 - 185 (1973)
bibtex data

Home page, Flashmode, TEXHelpers, TEX Switcher, pdfselect, TEX Scripts, Books, Preprints, Former Students, Veranstaltungen, Lecture Notes