The existence of \(k\)-convex hypersurface with prescribed mean curvature

DOI10.1007/s00526-010-0379-2zbMath1233.35074OpenAlexW2140732215MaRDI QIDQ635765

Xi-Nan Ma, Damin Wu, Fei Han

Publication date: 23 August 2011

Published in: Calculus of Variations and Partial Differential Equations (Search for Journal in Brave)

Full work available at URL: https://doi.org/10.1007/s00526-010-0379-2

zbMATH Keywords

elliptic partial differential equationsconstant rank theoremstar-shaped hypersurfaces

Mathematics Subject Classification ID

Second-order elliptic equations (35J15) Laplace operator, Helmholtz equation (reduced wave equation), Poisson equation (35J05) Differential geometry of immersions (minimal, prescribed curvature, tight, etc.) (53C42)

Related Items (11)

A regularity result for a class of non-uniformly elliptic operators ⋮ The eigenvalue problem for Hessian type operator ⋮ Interior $C^{2}$ estimates for the Hessian quotient type equation ⋮ The Neumann Problem for a Class of Fully Nonlinear Elliptic Partial Differential Equations ⋮ A constant rank theorem for spacetime convex solutions of heat equation ⋮ Hypersurfaces of prescribed mixed Weingarten curvature ⋮ A microscopic convexity principle for spacetime convex solutions of fully nonlinear parabolic equations ⋮ Curvature estimates for a class of Hessian quotient type curvature equations ⋮ Starshaped sets ⋮ On the microscopic spacetime convexity principle of fully nonlinear parabolic equations. I: Spacetime convex solutions ⋮ Positivity sets of supersolutions of degenerate elliptic equations and the strong maximum principle

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