Starshaped compact hypersurfaces in warped product manifolds II: a class of Hessian type equations

2024/05/08 by Bin Wang, Wang, Bin · 2 citations
Mathematics · #Analysis of PDEs (math.AP) #Differential Geometry (math.DG) #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.2405.04882

openalex publication_date 2024/05/08 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

Abstract

In this note, we prove the existence of one particular class of starshaped compact hypersurfaces, by deriving global curvature estimates for such hypersurfaces; this generalizes the main result in [Hypersurfaces of prescribed mixed Weingarten curvature. J. Geom. Anal. 34 (2024).] from the Euclidean space to Riemannian warped products. Moreover, we show that interior second order a priori estimates for admissible solutions to the associated fully nonlinear elliptic partial differential equations can be readily established by similar arguments.

Cited by

• Asymptotic Plateau problem for 2-convex hypersurface in ℍ⁴
• Novel Loss-Enhanced Universal Adversarial Patches for Sustainable Speaker Privacy

Related

• Starshaped compact hypersurfaces with prescirbed Weingarten curvature in warped product manifolds
• Starshaped compact hypersurfaces in warped product manifolds I: prescribed curvature equations
• A class of Hessian quotient equations in the warped product manifold
• On compact embbeded Weingarten hypersurfaces in warped products
• k-convex hypersurfaces with prescribed Weingarten curvature in warped product manifolds