时 间	地 点	报告人	题 目
2016年9月20日 10:30-11:30	蒙民伟楼1105室	袁伟(中山大学)	Q-曲率形变的稳定性与刚性结果及其应用 Q-曲率作为曲面上高斯曲率的高阶推广，最早由S.Paneitz及T.Branson在20世纪八 十年代发现。其后的三十多年中，众多数学家对Q-曲率的几何与分析性质做了深入的研究 。特别地，Q-曲率一直是共形几何中的重要研究对象之一，目前这方面的研究已经取得了 丰硕的成果。另一方面，作为一个纯粹的黎曼几何曲率量，有关Q-曲率的研究工作却不多 见。在本报告中，我们将着重从Q-曲率的黎曼几何性质着手，深入探讨其在度量模空间上 的局部几何结构，从而导出一些Q-曲率深入的几何性质。这些性质主要集中在其局部稳定 性与刚性性质上。应用这些结果，我们可以得到一些有关Q-曲率的深刻结果，这其中包括 环面的刚性定理以及Kazdan-Warner型存在定理等等。
2016年10月13日 10:30-11:30	蒙民伟楼1105室	王芳(上海交通大学)	Limit of sharp Sobolev inequalities We consider the sharp Sobolev inequalities on the n-sphere. By assuming the dimension constant to be a continuous parameter, then the limit of sharp Sobolev inequalities gives the Morse-Trudinger inequality as n goes to 2. However, this is a fake proof of the Morse-Trudinger since the dimension constant can only be an integer. In this talk, I will mainly introduce a new point of view to make the limit to be mathematically true, by taking advantage of the fractional GJMS operators and their energy extension to the hyperbolic space.
2016年10月18日 10:30-11:30	蒙民伟楼1105室	殷浩(中国科学技术大学)	Neck analysis of extrinsic polyharmonic maps We prove the energy identity and no neck property for a sequence of smooth extrinsic polyharmonic maps with bounded total energy.
2016年11月26日 14:00-16:00	蒙民伟楼1105室	夏超(厦门大学)	Reilly type formula and applications Bochner’s technique is one of most useful techniques in geometric analysis. In this talk, I will focus on the applications of integral version of Bochner's formula on manifolds with boundary, which is referred to Reilly’s formula, on geometric inequalities. Initiated by recent interest in studying geometric inequalities on warped product manifold, I will discuss my recent work on generalized Reilly type formula for sub-static manifolds. I will explain the formula from two points of view. One reflects a Bochner type technique on affine connection, the other reflects that in static space-time. Applications on geometric inequalities will be presented. The talk is based on joint work with Junfang Li at Birmingham.
2016年12月6日 10:30-11:30	蒙民伟楼1105室	金天灵(香港科技大学)	Holder gradient estimates for parabolic homogeneous p-Laplacian equations We prove interior Holder estimates for the spatial gradient of viscosity solutions to the parabolic homogeneous p-Laplacian equation \[ u_t=|\nabla u|^{2-p} div (|\nabla u|^{p-2}\nabla u), \] where 1< p<\infty. This equation arises from tug-of-war-like stochastic games with noise. It can also be considered as the parabolic p-Laplacian equation in non-divergence form. This is joint work with Luis Silvestre.