School of Mathematics and Statistics
Fuyang Normal University
Fuyang 236037, Anhui, China
email: zhou109@mail.ustc.edu.cn
Jundong Zhou
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.
DOI: https://doi.org/10.58997/ejde.2022.18
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Jundong Zhou School of Mathematics and Statistics Fuyang Normal University Fuyang 236037, Anhui, China email: zhou109@mail.ustc.edu.cn |
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