Stability of the area preserving mean curvature flow in asymptotic Schwarzschild space

IF 1.7 2区 数学 Q1 MATHEMATICS
Yaoting Gui , Yuqiao Li , Jun Sun
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引用次数: 0

Abstract

We first demonstrate that the area preserving mean curvature flow of hypersurfaces in space forms exists for all time and converges exponentially fast to a round sphere if the integral of the traceless second fundamental form is sufficiently small. Then we show that from sufficiently large initial coordinate sphere, the area preserving mean curvature flow exists for all time and converges exponentially fast to a constant mean curvature surface in 3-dimensional asymptotically Schwarzschild spaces. This provides a new approach to the existence of foliation established by Huisken and Yau ([11]). And also a uniqueness result follows.
渐近史瓦西空间中保面积平均曲率流的稳定性
首先证明了空间型超曲面的保面积平均曲率流始终存在,并且在无迹第二基本形式的积分足够小的情况下以指数速度收敛到一个圆球。然后证明了在足够大的初始坐标球上,保持面积的平均曲率流始终存在,并且在三维渐近史瓦西空间中以指数速度收敛到一个常平均曲率曲面。这为Huisken和Yau([11])建立的叶理存在提供了新的思路。这也是唯一性的结果。
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来源期刊
CiteScore
3.20
自引率
5.90%
发文量
271
审稿时长
7.5 months
期刊介绍: The Journal of Functional Analysis presents original research papers in all scientific disciplines in which modern functional analysis plays a basic role. Articles by scientists in a variety of interdisciplinary areas are published. Research Areas Include: • Significant applications of functional analysis, including those to other areas of mathematics • New developments in functional analysis • Contributions to important problems in and challenges to functional analysis
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