Horo-convex hypersurfaces with prescribed shifted Gauss curvatures in \(\pmb{\mathbb{H}}^{n+1}\)

DOI10.1007/S12220-020-00533-9zbMath1482.35103arXiv2007.14233OpenAlexW3093566488MaRDI QIDQ2048300

Qiang Tu, Li Chen, Kang Xiao

Publication date: 5 August 2021

Published in: The Journal of Geometric Analysis (Search for Journal in Brave)

Full work available at URL: https://arxiv.org/abs/2007.14233

zbMATH Keywords

second fundamental formMonge-Ampère type equationhoro-convex hypersurface

Mathematics Subject Classification ID

Surfaces in Euclidean and related spaces (53A05) Mixed volumes and related topics in convex geometry (52A39) Monge-Ampère equations (35J96)

Related Items (1)

\(\mathcal{M}\)-convex hypersurfaces with prescribed shifted Gaussian curvature in warped product manifolds

Cites Work

• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Closed hypersurfaces with prescribed Weingarten curvature in Riemannian manifolds
• Hypersurfaces of prescribed curvature measure
• A note on star-shaped compact hypersurfaces with prescribed scalar curvature in space forms
• Embedded hyperspheres with prescribed mean curvature
• Hypersurfaces in \(\mathbb H^{n+1}\) and conformally invariant equations: the generalized Christoffel and Nirenberg problems
• Starshaped compact hypersurfaces with prescribed \(k\)-th mean curvature in hyperbolic space
• Starshaped compact hypersurfaces with prescribed Weingarten curvature in warped product manifolds
• Convex hypersurfaces of prescribed curvatures
• Non-Negatively Curved Hypersurfaces of Hyperbolic Space and Subharmonic Functions
• Closed Weingarten hypersurfaces in warped product manifolds
• Degree Theory for Second Order Nonlinear Elliptic Operators and its Applications
• SOLUTION OF THE DIRICHLET PROBLEM FOR CURVATURE EQUATIONS OF ORDER $ m$
• The Existence of Convex Body with Prescribed Curvature Measures
• Classical solutions of fully nonlinear, convex, second-order elliptic equations
• Hypersurfaces in IRⁿ⁺¹with prescribed gaussian curvature and related equations of monge—ampére type
• On the curvature estimates for Hessian equations
• A Mean Curvature Type Flow in Space Forms
• Global C²‐Estimates for Convex Solutions of Curvature Equations
• Christoffel's problem for general convex bodies
• An interior estimate for convex solutions and a rigidity theorem

This page was built for publication: Horo-convex hypersurfaces with prescribed shifted Gauss curvatures in \(\pmb{\mathbb{H}}^{n+1}\)