THE WEIGHTED CONFORMAL MEAN CURVATURE FLOW

被引：0

作者：

Ho, Pak tung ^{[1
]}

Shin, Jinwoo ^{[2
]}

Yan, Zetian ^{[3
]}

机构：

[1] Tamkang Univ, Dept Math, New Taipei City 251301, Taiwan

[2] Sookmyung Womens Univ, Dept Math, Seoul 04310, South Korea

[3] Univ Calif Santa Barbara, Dept Math, Santa Barbara, CA 93106 USA

来源：

DISCRETE AND CONTINUOUS DYNAMICAL SYSTEMS | 2024年

关键词：

Key veords and phrases. Yamabe flow; manifolds with boundary; smooth metric measure space; YAMABE FLOW; CONVERGENCE; MANIFOLDS; DEFORMATION; EQUATIONS;

D O I：

10.3934/dcds.2024171

中图分类号：

O29 [应用数学];

学科分类号：

070104 ;

摘要：

We introduce a Yamabe-type flow ( partial derivative g R m partial derivative t =2( h m phi - H phi m ) g phi = 0 in M and partial derivative phi partial derivative t = m ( H phi m - h m phi ) on partial derivative M on a smooth metric measure space with boundary ( M, g, e - phi dV g , e - phi dA g , m ), where R m phi is the weighted scalar curvature, H phi m is the weighted mean curvature and h m phi is the average of the weighted mean curvature. We prove the long-time existence and convergence of this flow.

引用

页码：2446 / 2470

页数：25

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