A class of Hessian quotient equations in warped product manifolds  

作　　者：Weimin Sheng Ke Xue 

机构地区：[1]School of Mathematical Sciences,Zhejiang University,Hangzhou 310058,China

出　　处：《Science China Mathematics》2025年第3期637-648,共12页中国科学(数学英文版)

基　　金：supported by National Key R&D Program of China(Grant No.2022YFA1005500);National Natural Science Foundation of China(Grant Nos.12031017 and 11971424)。

摘　　要：Given a compact Riemannian manifold M and an open interval I in R,we consider a warped product manifold M=I×φM.For a positive function f defined on M,we obtain the existence of the(η,k)-convex hypersurfaceΣwhich satisfies a Hessian quotient equationσk(λ(η))/σl(λ(η))=f(V,ν(V))for 0≤l<k<n,andη=Hg-h,the first Newton transformation of the second fundamental form h.This generalizes the result of Chen et al.(2020)and gives a simpler proof of the curvature estimate.As a corollary,we can get an(η,k)-convex solution for f(V,ν)=|V^(|-n-1)h(V/|V|)in R^(n+1)for some prescribed function h,which can be viewed as the prescribed curvature measure type problem.

关 键 词：warped product manifold (η k)-convex curvature equation 

分 类 号：O186.1[理学—数学]