讲座问题：完全非线性偏微分方程理论中的下解和凹性
主 讲 人：关波 教授 美国俄亥俄州立大学 厦门大学
讲座时间：2017年12月25日（周一）下昼14：00
讲座所在：阜成路东校区1号楼二层理学院聚会室
加入工具：理学院数学系西席、研究生
主理单位：研究生院
承办单位：理学院
主讲人简介：
波教授，美国俄亥俄州立大学教授，厦门大学长江讲座教授。其研究领域为完全非线性偏微分方程及其相关几何问题。在国际顶尖数学杂志 Annals of Math. Comm. Pure. Appl. Math, J. Differential, Geometry., Adv. Math. 等杂志揭晓论文30余篇。
主讲内容：
Fully nonlinear elliptic and parabolic equations on manifolds play central roles in some important problems in real and complex geometry. A key ingredient in solving such equations is to establish a priori estimates up to second order. For general Riemannian manifolds, or Kahler/Hermitian manifolds in the complex case, one encounters difficulties caused by the curvature (as well as torsion in the Hermian case) of the manifolds. In this talk we report some results in our effort to overcome these obstacles over the past few years. We shall emphasize on understanding the roles of subsolutions and concavity of the equation based on which our techniques were developed. We are interested both in equations on closed manifolds, and in the Dirichlet problem for equations on manifolds with boundary, without imposing any restrictions to the geometry of the boundary.