Two problems related to prescribed curvature measures

TL;DR

This paper explores the existence of convex bodies with prescribed generalized curvature measures using advanced techniques, and also enhances existing $C^2$ estimates for prescribed curvature equations.

Contribution

It introduces new existence results for convex bodies with prescribed curvature measures and improves $C^2$ estimates using Guan-Li-Li's innovative methods.

Findings

Established existence of convex bodies with prescribed curvature measures.

Enhanced $C^2$ estimates for prescribed curvature equations.

Abstract

Existence of convex body with prescribed generalized curvature measures is discussed, this result is obtained by making use of Guan-Li-Li's innovative techniques. In surprise, that methods has also brought us to promote Ivochkina's $C^2$ estimates for prescribed curvature equation in \cite{I1, I}.