Electronic Journal of Differential Equations, Vol. 2022 (2022), No. 18, pp. 1-14.

Title: k-Hessian curvature type equations in space forms
       
Authors: Jundong Zhou (Fuyang Normal Univ., Anhui, China)

Abstract:  
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 Hessian 
curvature type equations. Secondly, we obtain an existence result by using standard degree 
theory based on a priori estimates.

Submitted April 1, 2021. Published March 10, 2022.
Math Subject Classifications: 53A99, 35J60.
Key Words: A priori estimate; curvature type equation; (eta, k)-convex; star-shape; space form.