Maximum principle for hypersurfaces

DOI10.1007/BF01182085zbMath0678.53048OpenAlexW2056168511MaRDI QIDQ1124136

Jost-Hinrich Eschenburg

Publication date: 1989

Published in: Manuscripta Mathematica (Search for Journal in Brave)

Full work available at URL: https://eudml.org/doc/155396

zbMATH Keywords

maximum principletotally geodesicmean curvaturesgeneralized mean curvature

Mathematics Subject Classification ID

Differential geometry of immersions (minimal, prescribed curvature, tight, etc.) (53C42) Global submanifolds (53C40) Global differential geometry of Lorentz manifolds, manifolds with indefinite metrics (53C50)

Related Items (14)

Conformal vector fields and null hypersurfaces ⋮ Mean convex properly embedded \([ \varphi , \vec{e}_3 \)-minimal surfaces in \(\mathbb{R}^3\)] ⋮ On the topology of translating solitons of the mean curvature flow ⋮ A barrier principle at infinity for varifolds with bounded mean curvature ⋮ Characterizations of spacelike hyperplanes in the steady state space via generalized maximum principles ⋮ Achronal limits, Lorentzian spheres, and splitting ⋮ A sharp comparison theorem for compact manifolds with mean convex boundary ⋮ Regularity of Lorentzian Busemann Functions ⋮ On mean-convex Alexandrov embedded surfaces in the 3-sphere ⋮ \(f\)-minimal surface and manifold with positive \(m\)-Bakry-Émery Ricci curvature ⋮ On the topology of black holes ⋮ Codimension two spacelike submanifolds through a null hypersurface in a Lorentzian manifold ⋮ Equilibrium of surfaces in a vertical force field ⋮ Null hypersurfaces and the rigged metric

Cites Work

• An extension of E. Hopf's maximum principle with an application to Riemannian geometry
• An elementary proof of the Cheeger-Gromoll splitting theorem
• Uniqueness, symmetry, and embeddedness of minimal surfaces
• Comparison theorems and hypersurfaces
• The splitting theorem for space-times with strong energy condition
• Minimal surfaces and 3-manifolds of non-negative Ricci curvature
• The Lorentzian splitting theorem without the completeness assumption
• Eigenvalue comparison theorems and its geometric applications
• The splitting theorem for manifolds of nonnegative Ricci curvature
• On the structure of complete manifolds of nonnegative curvature
• A Sphere Theorem for Manifolds of Positive Ricci Curvature
• The Large Scale Structure of Space-Time
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