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

List of publications (pdf)

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)
To appear in Am. J. Math.
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)
June 13, 2008
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)
July 30, 2009
also available from arXiv:0907.5403

An energy gap for Yang-Mills connections (pdf)
August 6, 2009
also available from arXiv:0908.0767

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