Starshaped compact hypersurfaces in warped product manifolds I: prescribed curvature equations

2024/04/30 by Bin Wang, Wang, Bin
Mathematics · #Analysis of PDEs (math.AP) #FOS: Mathematics #Geometric Analysis and Curvature Flows #Geometric and Algebraic Topology #Geometry and complex manifolds #Primary 53C21 #Secondary 35J60

paper · pdf · doi:10.48550/arxiv.2404.19562

openalex publication_date 2024/04/30 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

Abstract

We derive global curvature estimates for closed, strictly star-shaped (n-2)-convex hypersurfaces in warped product manifolds, which satisfy the prescribed (n-2)-curvature equation with a general right-hand side. The proof can be readily adapted to establish curvature estimates for semi-convex solutions to the general k-curvature equation. Furthermore, it can also be used to prove the same estimates for k-convex solutions to the prescribed curvature measure type equations.

Related

• Starshaped compact hypersurfaces in warped product manifolds II: a class of Hessian type equations
• k-convex hypersurfaces with prescribed Weingarten curvature in warped product manifolds
• Starshaped compact hypersurfaces with prescirbed Weingarten curvature in warped product manifolds
• Curvature estimates for p-convex hypersurfaces of prescribed curvature
• On compact embbeded Weingarten hypersurfaces in warped products