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

List of publications (pdf)

My papers on arXiv

Hypersurfaces of prescribed mean curvature over obstacles (pdf)
Math. Z. 133, 169 - 185 (1973)
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Regularity of solutions of nonlinear variational inequalities (pdf)
Arch. Rat. Mech. Analysis 52, 389 - 393 (1973)
 

Existence, regularity, and boundary behaviour of generalized surfaces of prescribed mean curvature (pdf)
Math. Z. 139, 173 - 198 (1974)
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Global regularity of the solutions to the capillarity problem (pdf)
Ann. Sc. Norm. Sup. Pisa, Ser. IV, 3, 157 - 175 (1976)

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

H-surfaces in Lorentzian manifolds (pdf)
Commun. Math. Phys. 89, 523 - 553 (1983)
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Global $C^{1,1}$-regularity for solutions to quasi-linear variational inequalities (pdf)
Arch. Rat. Mech. Analysis 89, 83 - 92 (1985)
 

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

Closed Weingarten hypersurfaces in Riemannian manifolds (pdf)
Journal Diff. Geom. 43, 612 - 641 (1996)
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Closed Weingarten hypersurfaces in space forms (pdf)
Geometric Analysis and the Calculus of Variations (J. Jost, ed.),  International Press, Boston, pp. 71 - 98 (1996)
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Hypersurfaces of prescribed Weingarten curvature (pdf)
Math. Z.  224, 167 - 194 (1997)
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Erratum: Hypersurfaces of prescribed Weingarten curvature (pdf)
Math. Z.  233, 829 - 830 (2000)
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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
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On the foliation of space-time by constant mean curvature hypersurfaces (pdf)
March 21, 1999
also available from math.DG/0304423
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Hypersurfaces of prescribed mean curvature in Lorentzian manifolds (pdf)
Math. Z.  235, 83 - 97 (2000)
also available from math.DG/0409465
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Hypersurfaces of prescribed curvature in Lorentzian manifolds (pdf)
Indiana Univ. Math. J. 49, 1125 - 1152 (2000)
also available from math.DG/0409457
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Hypersurfaces of prescribed scalar curvature in Lorentzian manifolds (pdf)
J. reine angew. Math. 554, 157 - 199 (2003)
also available from math.DG/0207054
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Closed Weingarten hypersurfaces in semi-riemannian manifolds (pdf)
November 6, 2001
also available from math.DG/0207053
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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
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The mass of a Lorentzian manifold (pdf)
Adv. Theor. Math. Phys. 10, 33 - 48 (2006)
also available from math.DG/0403002
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The inverse mean curvature flow in cosmological spacetimes (pdf)
Adv. Theor. Math. Phys. 12, 1183 - 1207 (2008)
also available from math.DG/0403097
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The inverse mean curvature flow in ARW spaces - transition from big crunch to big bang (pdf)
also available from math.DG/0403485
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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
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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
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On the CMC foliation of future ends of a spacetime (pdf)
Pacific J. Math. 226, 297 - 308 (2006)
also available from math.DG/0408197
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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
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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
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Minkowski type problems for convex hypersurfaces in hyperbolic space (pdf)
February 27, 2006
also available from math.DG/0602597
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Curvature flows in semi-Riemannian manifolds (pdf)
Surveys in Differential Geometry XII, 113 - 165 (2008)
also available from arXiv:0704.0236

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

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

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

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 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

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

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

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

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

Non-scale-invariant inverse curvature flows in Euclidean space (pdf)
iPad version
May 31, 2011
also available from arXiv:1112.5626

A note on inverse curvature flows in ARW spacetimes (pdf)
iPad version
June 21, 2011
also available from arXiv:1106.4236

The quantization of gravity in globally hyperbolic spacetimes (pdf)
iPad version
May 7, 2012
also available from arXiv:1205.1427

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