学术报告
【学术报告】Geometric Analysis Seminar: Conformally invariant elliptic equations: Liouville and Yamabe
编辑:刘梦洁发布时间:2023年05月29日


报告人:初保志Rutgers University-New Brunswick

间:20236111:00

点:海韵园实验楼105报告厅

内容摘要:

For dimension n 3, there is a classic result due to Liouville:

u = 0, u > 0, R n u constant.

There is also a renowned Liouville-type theorem for Yamabe equation due to Caffarelli-Gidas-Spruck (under additional conditions, by Obata and Gidas-Ni-Nirenberg):

4B8A

In a joint work with Yanyan Li and Zongyuan Li, we generalize both Liouville-type theorems above along the direction of conformal invariance to the fully nonlinear version. And our both generalized theorems are necessary and sufficient statements by realizing the same borderline. We expect they will be useful in treating scalar curvature changing-sign problems in conformal geometry. If time permits, I will also discuss some applications of our Liouville Theorems, including local gradient estimates, Harnack inequalities, etc.

人简介

初保志2019年本科毕业于厦门大学,现博士就读于Rutgers University-New Brunswick, 师从李岩岩教授。


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