## 数学与统计及交叉学科前沿论坛------高端学术讲座第64场

向妮，湖北大学数学与统计学学院教授，博士生导师。主要研究完全非线性偏微分方程等，在Calc. Var. Partial Differential Equations，J. Differential Equations, Proc. of the Royal Society of Edinburgh等发表学术论文多篇，主持湖北省万博matext官网登录-首頁(歡迎您)厅优秀中青年人才项目两项，国家自然科学基金天元基金、青年基金、面上项目各一项。

In this talk, we introduce the second order derivative estimates for Hessian equations $\sigma_k(u_{ij}+u\delta_{ij})=f(x, u, \nabla u)$ on $\mathbb{S}^n$, which can be regarded as an generalization of Christoffel-Minkowski type problems. Furthermore, we derive the existence and uniqueness results for convex solution of general Christoffel-Minkowski problem $\sigma_k(u_{ij}+u\delta_{ij})=\varphi(x)g(u)$ based on the a priori estimates and constant rank theorem.