k-Hessian curvature type equations in space forms

Electronic Journal of Differential Equations

article

Jundong Zhou¹ 

[1] School of Mathematics and Statistics Fuyang Normal University Fuyang 236037

关键词: A priori estimate;    curvature type equation;    (eta;    k)-convex;    star-shape;    space form.;   

DOI  :  10.58997/ejde.2022.18

学科分类：数学（综合）

来源: Texas State University

【 摘 要 】

In this article, we study closed star-shaped (eta, k)-convex hypersurfaces in space forms satisfying a class of k-Hessian curvature type equations.Firstly, using the maximum principle, we obtain a priori estimates for the class of Hessiancurvature type equations. Secondly, we obtain an existence result by using standard degreetheory based on a priori estimates.

【 授权许可】

CC BY