ISOPERIMETRY AND VOLUME PRESERVING STABILITY IN REAL PROJECTIVE SPACES

被引：0

作者：

Viana, Celso ^{[1
]}

机构：

[1] Univ Fed Minas Gerais, Dept Math, BR-30123970 Belo Horizonte, MG, Brazil

来源：

JOURNAL OF DIFFERENTIAL GEOMETRY | 2023年 / 125卷 / 01期

关键词：

CONSTANT MEAN-CURVATURE; INDEX ONE; HYPERSURFACES; REGULARITY; THEOREMS; SURFACES; DENSITY; DOMAINS;

D O I：

暂无

中图分类号：

O1 [数学];

学科分类号：

0701 ; 070101 ;

摘要：

We classify the volume preserving stable hypersurfaces in the real projective space RPn. As a consequence, the solutions of the isoperimetric problem are tubular neighborhoods of projective subspaces RPk subset of RPn (starting with points). This confirms a conjecture of Burago and Zalgaller from 1988 and extends to higher dimensions previous result of M. Ritore and A. Ros on RP3. We also derive an Willmore type inequality for antipodal invariant hypersurfaces in S-n.

引用

页码：187 / 205

页数：19

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