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Academy of Mathematics and Systems Science, CAS Colloquia & Seminars：Liouville Properties on gradient shrinking Ricci solitons with constant scalar curvature
常标量 曲率梯度收缩 Ricci孤子 Liouville性质
2023/11/13
In this talk we show that bounded harmonic functions are constant on gradient shrinking Ricci solitons with CSC by frequency function method. As an application, we show that the space of harmonic func...
Academy of Mathematics and Systems Science, CAS Colloquia & Seminars：Some recent progress on the gradient estimates for the insulated conductivity problem
绝缘 电导率 梯度估计 椭圆偏微分方程
2023/4/17
In this talk, I will describe an elliptic PDE that models electric conduction, and the electric field concentration phenomenon between closely spaced inclusions of high contrast. In the first part, I ...
Academy of Mathematics and Systems Science, CAS Colloquia & Seminars：O(2)-symmetry of 3D steady gradient solitons
O(2) 三维稳态 梯度孤子 对称性
2023/4/13
In this talk, we talk about the proof of the O(2)-symmetry of 3D steady gradient solitons. The proof consists of four parts: the asymptotic analysis at infinity, the symmetry improvement theorem, the ...
Academy of Mathematics and Systems Science, CAS Colloquia & Seminars：Construction of steady gradient solitons by interpolation
插值 稳态梯度孤子 坍塌式
2023/4/13
In this talk, we give an overall description of the construction of the collapsed flying-wing-like steady gradient solitons, as well as the high dimension non-collapsed steady gradient solitons. In pa...
Academy of Mathematics and Systems Science, CAS Colloquia & Seminars：Primal Dual Alternating Proximal Gradient Algorithms for Nonsmooth Nonconvex Minimax Problems with Coupled Linear Constraints
耦合 线性约束 非光滑 非凸极小问题 基本对偶交替 近端梯度算法
2023/4/14
Nonconvex minimax problems have attracted wide attention in machine learning, signal processing and many other fields in recent years. In this paper, we propose a primal dual alternating proximal grad...
Academy of Mathematics and Systems Science, CAS Colloquia & Seminars：Steady gradient Ricci solitons with positive curvature
正曲率 稳态梯度 利玛窦孤子
2023/4/17
We will construct some new examples of steady gradient Ricci solitons with positive curvature operator. Moreover, for any 3D steady gradient Ricci soliton with positive curvature, if it is asymptotic ...