讲座人简介：

邱国寰，现任中国科学院数学与系统科学研究院副研究员，博士生导师。主要从事完全非线性椭圆方程方面的研究工作，在《Comm. Math. Phy.》、《Duke Math. J.》、《Amer. J. Math.》、《Int. Math. Res. Not.》等国际知名数学期刊上发表过多篇论文。曾于2019年获得中国数学会钟家庆奖，2021年入选国家海外青年人才计划。

讲座简介:

In this talk, I will present an in-depth analysis of interior C^2 estimates for the sigma_2-Hessian equation in three-dimensional Euclidean space. The discussion will focus on two key analytical tools: a trace-adjusted Jacobi inequality and a geometric doubling lemma. These tools are fundamentally important for studying the regularity properties of sigma_2-Hessian equations, which originate from isometric embedding problems in differential geometry and serve as a model equation for scalar curvature problems on hypersurfaces.