Starshaped compact hypersurfaces with prescirbed Weingarten curvature in warped product manifolds

2017/04/30 by Chen, Daguang, Li, Haizhong, Wang, Zhizhang
#Analysis of PDEs (math.AP) #Differential Geometry (math.DG) #FOS: Mathematics

paper · doi:10.48550/arxiv.1705.00313

Abstract

Given a compact Riemannian manifold M, we consider a warped product M = I ×_h M where I is an open interval in \Bbb R. For a positive function ψ defined on M, we generalized the arguments in \citeGRW2015 and \citeRW16, to obtain the curvature estimates for Hessian equations σ_k(κ)=ψ(V,ν(V)). We also obtain some existence results for the starshaped compact hypersurface Σ satisfying the above equation with various assumptions.

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