A New Proof of a Characterization of Small Spherical Caps

被引：0
|
作者：
Rafael López
机构：
[1] Universidad de Granada,Departamento de Geometría y Topología
来源：
Results in Mathematics | 2009年 / 55卷
关键词：
53A10; Mean curvature; maximum principle; spherical cap;
D O I：
暂无
中图分类号：
学科分类号：
摘要：
It is known that planar disks and small spherical caps are the only constant mean curvature graphs whose boundary is a round circle. Usually, the proof invokes the Maximum Principle for elliptic equations. This paper presents a new proof of this result motivated by an article due to Reilly. Our proof utilizes a flux formula for surfaces with constant mean curvature together with integral equalities on the surface.
引用
收藏
相关论文
共 50 条
  • [1] A New Proof of a Characterization of Small Spherical Caps
    Lopez, Rafael
    RESULTS IN MATHEMATICS, 2009, 55 (3-4) : 427 - 436
  • [2] NEW METHOD FOR COMPUTING AXISYMMETRIC BUCKLING OF SPHERICAL CAPS
    THURSTON, GA
    JOURNAL OF APPLIED MECHANICS, 1971, 38 (01): : 179 - &
  • [3] SPHERICAL DESIGNS FOR APPROXIMATIONS ON SPHERICAL CAPS
    Li, Chao
    Chen, Xiaojun
    SIAM JOURNAL ON NUMERICAL ANALYSIS, 2024, 62 (06) : 2506 - 2528
  • [4] Codes in spherical caps
    Barg, Alexander
    Musin, Oleg R.
    ADVANCES IN MATHEMATICS OF COMMUNICATIONS, 2007, 1 (01) : 131 - 149
  • [5] STRESSES IN SPHERICAL CAPS
    TABAKMAN, HD
    MACHINE DESIGN, 1977, 49 (05) : 79 - 82
  • [6] A CHARACTERIZATION OF CAPILLARY SPHERICAL CAPS BY A PARTIALLY OVERDETERMINED PROBLEM IN A HALF BALL
    Jia, Xiaohan
    Lu, Zheng
    Xia, Chao
    Zhang, Xuwen
    PROCEEDINGS OF THE AMERICAN MATHEMATICAL SOCIETY, 2025, 153 (01) : 161 - 170
  • [7] A characteristic property of spherical caps
    Ripoll, Jaime
    GEOMETRIAE DEDICATA, 2008, 133 (01) : 1 - 5
  • [8] ELECTROMAGNETIC INDUCTION IN SPHERICAL CAPS
    SCHWARTZ, K
    SCHUBERT, G
    TRANSACTIONS-AMERICAN GEOPHYSICAL UNION, 1974, 55 (04): : 228 - 228
  • [9] DEFLECTION AND SNAPPING OF SPHERICAL CAPS
    BRODLAND, GW
    COHEN, H
    INTERNATIONAL JOURNAL OF SOLIDS AND STRUCTURES, 1987, 23 (10) : 1341 - &
  • [10] Spherical Caps in Cell Polarization
    Diegmiller, Rocky
    Montanelli, Hadrien
    Muratov, Cyrill B.
    Shvartsman, Stanislav Y.
    BIOPHYSICAL JOURNAL, 2018, 115 (01) : 26 - 30
12345