Hypersurfaces of prescribed curvature in Lorentzian manifolds

DOI10.1512/iumj.2000.49.1861zbMath1034.53064arXivmath/0409457OpenAlexW2059781372WikidataQ126073924 ScholiaQ126073924MaRDI QIDQ2710412

Claus Gerhardt

Publication date: 2000

Published in: Indiana University Mathematics Journal (Search for Journal in Brave)

Full work available at URL: https://arxiv.org/abs/math/0409457

zbMATH Keywords

a priori estimatesstationary solutioncurvature flowprescribed curvatureWeingarten hypersurface

Mathematics Subject Classification ID

Nonlinear elliptic equations (35J60) Elliptic equations on manifolds, general theory (58J05) Differential geometry of immersions (minimal, prescribed curvature, tight, etc.) (53C42)

Related Items (13)

Curvature estimates of hypersurfaces in the Minkowski space ⋮ The global curvature estimate for the \(n - 2\) Hessian equation ⋮ Entire downward solitons to the scalar curvature flow in Minkowski space ⋮ Locally constrained inverse mean curvature flow in GRW spacetimes ⋮ Neumann and second boundary value problems for Hessian and Gauß curvature flows ⋮ Prescribing Gauss curvature of surfaces in 3-dimensional spacetimes. Application to the Minkowski problem in the Minkowski space ⋮ A note on inverse mean curvature flow in cosmological spacetimes ⋮ Inverse curvature flows in asymptotically Robertson Walker spaces ⋮ Parabolic approaches to curvature equations ⋮ The initial and Neumann boundary value problem for a class parabolic Monge-Ampère equation ⋮ Entire spacelike hypersurfaces of constant Gauß curvature in Minkowski space ⋮ Prescribed k-symmetric curvature hypersurfaces in de Sitter space ⋮ Estimates for the volume of a Lorentzian manifold

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