中国科学院数学与系统科学研究院

数学研究所

数学科学全国重点实验室

偏微分方程研讨班

Speaker: 周星晨 （清华大学）

Inviter: 邱国寰

Language: Chinese

Title：An Integral Approach to Prescribing Scalar Curvature Equations

Time&Venue：2025年12月2日(星期二) 9:20-10:20&思源楼S625

Abstract: In this talk, we will introduce a new integral approach to obtain interior a priori C1,1 estimates for convex solutions of prescribing scalar curvature equations as well as the quadratic Hessian equations σ2=f(x) in general dimensions. We prove that the C1.1 modules of the solutions depend only on the Lipschitz modules of f(x) instead of the ‖f‖Ck for some k≥2  in all the papers we have known up to now. The talk is based on a joint work with Chen Ruosi and Jian Huaiyu.

Speaker: 马文信 （南方科技大学）

Language: Chinese

Title：Compactness and Finiteness Theorems on the space of Rotationally Symmetric Self-Shrinkers

Time&Venue：2025年12月2日(星期二) 10:30-11:30&思源楼S625

Abstract: In this talk, we study the space of complete embedded rotationally symmetric self-shrinking hypersurfaces in Euclidean spaces. First, we derive explicit upper bounds for the entropy of all such self-shrinkers. Second, as an application we prove a smooth compactness theorem on the space of all such shrinkers. We also prove that there are only finitely many such self-shrinkers with an extra reflection symmetry.