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魏国栋、江瑞奇副教授学术报告(2020.12.10)

时间:2020-12-07 点击数:

bg真人学术报告


报告题目:On Gromov’s conjecture of fill-ins with nonnegative scalar curvature

报告人:魏国栋助理教授(中山大学)

报告时间:2020年12月10日 周四14:00-15:30

报告地点:(腾讯会议ID:832 895 424)

摘要:

In this talk,we first prove the extensibility of an arbitrary boundary metric to a positive scalar curvature metric inside for a compact manifold with boundary, which solves an open problem due to Gromov. Then we introduce a fill-in invariant and discuss its relationship with the positive mass theorems for asymptotically flat (AF) and asymptotically hyperbolic (AH) manifolds. In particular, we prove that the positive mass theorem for AH manifolds implies that for AF manifolds. In the end, we give some estimates for the fill-in invariant, which provide some partially affirmative answers to two conjectures by Gromov. This is a joint work with Prof. Yuguang Shi and Dr. Wenlong Wang.

报告人简介:

魏国栋助理教授的研究方向为几何分析,特别是数量曲率的几何以及Willmore泛函的极小变分问题,目前已在Math. Ann., J. Geom. Anal., Asian J. Math等学术期刊上发表论文数篇。



报告题目:Existence of polyharmonic maps in critical dimensions

报告人:江瑞奇副教授(湖南大学)

报告时间:2020年12月10日 周四15:30-17:00

报告地点:(腾讯会议ID:832 895 424)

摘要:

In this talk, we show that for any two closed Riemannian manifolds M^m and N, there

exists a minimizing (extrinsic) m-polyharmonic map for every free homotopy class in

[M^{2m},N], provided that the homotopy group \pi_{2m}(N) is trivial. This generalizes the celebrated existence results for harmonic maps and biharmonic maps. We also prove that there exists a non-constant smooth polyharmonic map from R^{2m} to N by a blowup analysis at an energy-concentration point for an energy-minimizing sequence if the convergence fails to be strong.

报告人简介:

江瑞奇副教授的研究方向为几何分析,特别是几何偏微分方程解的存在性与正则性问题,相关结果发表在J. Funct. Anal.,Discrete Contin. Dyn. Syst.,Asian J. Math.等学术期刊上。


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会议时间:2020/12/10 14:00-17:00

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会议ID:832 895 424

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