A half-space type property in the Euclidean sphere

IF 0.5 Q3 MATHEMATICS
M. Velásquez
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引用次数: 0

Abstract

. We study the notion of strong r -stability for the context of closed hypersurfaces Σ n ( n ≥ 3) with constant ( r + 1)-th mean curvature H r +1 immersed into the Euclidean sphere S n +1 , where r ∈ { 1 ,...,n − 2 } . In this setting, under a suitable restriction on the r -th mean curvature H r , we establish that there are no r -strongly stable closed hypersurfaces immersed in a certain region of S n +1 , a region that is determined by a totally umbilical sphere of S n +1 . We also provide a rigidity result for such hypersurfaces.
欧几里得球的半空间型性质
。我们研究了闭超曲面Σ n (n≥3)的强r -稳定性的概念,该闭超曲面具有常数(r +1)-平均曲率H r +1浸入欧几里得球S n +1,其中r∈{1,…,n−2}。在这种情况下,在对r -平均曲率H的适当限制下,我们建立了在S n +1的某一区域中不存在r -强稳定闭超曲面,该区域由S n +1的完全脐带球确定。我们还提供了这种超曲面的刚性结果。
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来源期刊
Archivum Mathematicum
Archivum Mathematicum MATHEMATICS-
CiteScore
0.70
自引率
16.70%
发文量
0
审稿时长
35 weeks
期刊介绍: Archivum Mathematicum is a mathematical journal which publishes exclusively scientific mathematical papers. The journal, founded in 1965, is published by the Department of Mathematics and Statistics of the Faculty of Science of Masaryk University. A review of each published paper appears in Mathematical Reviews and also in Zentralblatt für Mathematik. The journal is indexed by Scopus.
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