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

2026/07/16 by Kang Xiao, Jiabao Gong
#math.DG #math.AP

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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.

Citations

• Global C2‐Estimates for Convex Solutions of Curvature Equations
• Convexity estimates for mean curvature flow and singularities of mean convex surfaces

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