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arXiv · 2607.14717

The existence of $k$-convex hypersurface for a class of Hessian curvature equations

Kang Xiao·Jiabao Gong
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Abstract

This article investigates the existence of closed, star-shaped hypersurfaces for a class of Hessian curvature equations. By combining a priori estimates with the continuity method, we establish the existence and uniqueness of $k$-convex hypersurfaces for both nonhomogeneous and homogeneous Hessian curvature equations, and by establishing a constant rank theorem, we prove that the resulting $k$-convex hypersurfaces are strictly convex.

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Kang Xiao, Jiabao Gong. 2026-07-16. The existence of $k$-convex hypersurface for a class of Hessian curvature equations. https://arxiv.org/abs/2607.14717

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