Closed hypersurfaces with prescribed Weingarten curvature in Riemannian manifolds

DOI10.1007/s00526-012-0540-1zbMath1285.53047OpenAlexW2024665611WikidataQ115387478 ScholiaQ115387478MaRDI QIDQ368554

Qi-Rui Li, Weimin Sheng

Publication date: 23 September 2013

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

Full work available at URL: https://doi.org/10.1007/s00526-012-0540-1

zbMATH Keywords

curvature functiongradient estimatesGauss-Weingarten relationsglobal normal Gaussian coordinate systemWeingarten curvature

Mathematics Subject Classification ID

Nonlinear elliptic equations (35J60) Differential geometry of immersions (minimal, prescribed curvature, tight, etc.) (53C42)

Related Items (7)

\(\mathcal{M}\)-convex hypersurfaces with prescribed shifted Gaussian curvature in warped product manifolds ⋮ Prescribed \(L_p\) curvature problem ⋮ Starshaped compact hypersurfaces with prescribed Weingarten curvature in warped product manifolds ⋮ Parabolic approaches to curvature equations ⋮ A class of prescribed Weingarten curvature equations in Euclidean space ⋮ A class of Hessian quotient equations in Euclidean space ⋮ Horo-convex hypersurfaces with prescribed shifted Gauss curvatures in \(\pmb{\mathbb{H}}^{n+1}\)

Cites Work

• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Interior curvature bounds for a class of curvature equations
• Embedded hyperspheres with prescribed mean curvature
• Starshaped compact hypersurfaces with prescribed \(k\)-th mean curvature in hyperbolic space
• Closed Weingarten hypersurfaces in Riemannian manifolds
• Contraction of convex hypersurfaces in Euclidean space
• Hypersurfaces of prescribed Weingarten curvature
• Minimal varieties in Riemannian manifolds
• Closed Weingarten hypersurfaces in warped product manifolds
• Degree Theory for Second Order Nonlinear Elliptic Operators and its Applications
• Curvature estimates for Weingarten hypersurfaces in Riemannian manifolds
• A general existence proof for non-linear elliptic equations in semi-Riemannian spaces
• Christoffel's problem for general convex bodies

This page was built for publication: Closed hypersurfaces with prescribed Weingarten curvature in Riemannian manifolds