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
收藏
页码：187 / 205
页数：19
相关论文
共 50 条
  • [1] Orthogonality preserving bijective maps on real and complex projective spaces
    Rodman, Leiba
    Semrl, Peter
    LINEAR & MULTILINEAR ALGEBRA, 2006, 54 (05): : 355 - 367
  • [2] On canonical embeddings of complex projective spaces in real projective spaces
    Konnov V.V.
    Journal of Mathematical Sciences, 2007, 142 (5) : 2367 - 2376
  • [3] Spaces of algebraic maps from real projective spaces into complex projective spaces
    Kozlowski, Andrzej
    Yamaguchi, Kohhei
    HOMOTOPY THEORY OF FUNCTION SPACES AND RELATED TOPICS, 2010, 519 : 145 - +
  • [4] EMBEDDING REAL PROJECTIVE SPACES
    MAHOWALD, M
    MILGRAM, RJ
    ANNALS OF MATHEMATICS, 1968, 87 (03) : 411 - &
  • [5] Real projective spaces are nonfibrators
    Daverman, RJ
    TOPOLOGY AND ITS APPLICATIONS, 1999, 94 (1-3) : 61 - 66
  • [6] On the genus of real projective spaces
    Cavicchioli, Alberto
    Spaggiari, Fulvia
    ARCHIV DER MATHEMATIK, 2007, 89 (06) : 570 - 576
  • [7] Packings in Real Projective Spaces
    Fickus, Matthew
    Jasper, John
    Mixon, Dustin G.
    SIAM JOURNAL ON APPLIED ALGEBRA AND GEOMETRY, 2018, 2 (03): : 377 - 409
  • [8] STUNTED REAL PROJECTIVE SPACES
    JAMES, IM
    SUTHERLA.WA
    QUARTERLY JOURNAL OF MATHEMATICS, 1974, 25 (97): : 101 - 112
  • [9] THE LEVEL OF REAL PROJECTIVE SPACES
    STOLZ, S
    COMMENTARII MATHEMATICI HELVETICI, 1989, 64 (04) : 661 - 674
  • [10] On the genus of real projective spaces
    Alberto Cavicchioli
    Fulvia Spaggiari
    Archiv der Mathematik, 2007, 89 : 570 - 576
12345