On minimal surfaces bounded by two convex curves in parallel planes

被引：3
|
作者：
Traizet, Martin [1 ]
机构：
[1] Univ Tours, Lab Math & Phys Theor, F-37200 Tours, France
来源：
COMMENTARII MATHEMATICI HELVETICI | 2010年 / 85卷 / 01期
关键词：
Minimal surface with boundary; Robin function; concentration of curvature; CURVATURE; EMBEDDEDNESS; COMPACTNESS; STATIONARY;
D O I：
10.4171/CMH/187
中图分类号：
O1 [数学];
学科分类号：
0701 ; 070101 ;
摘要：
We prove that a compact minimal surface bounded by two closed convex curves in parallel planes close enough to each other must be topologically an annulus.
引用
收藏
页码：39 / 71
页数：33
相关论文
共 50 条
  • [11] Triply periodic minimal surfaces bounded by vertical symmetry planes
    Fujimori, Shoichi
    Weber, Matthias
    MANUSCRIPTA MATHEMATICA, 2009, 129 (01) : 29 - 53
  • [12] TYPICAL CONVEX CURVES ON CONVEX SURFACES
    ZAMFIRESCU, T
    MONATSHEFTE FUR MATHEMATIK, 1987, 103 (03): : 241 - 247
  • [13] The minimal and convex surfaces
    Taskarayev, A.
    Abzhapbarov, A.
    Ashirbayev, N. K.
    BULLETIN OF THE KARAGANDA UNIVERSITY-MATHEMATICS, 2015, 78 (02): : 145 - 151
  • [14] Stability of anisotropic capillary surfaces between two parallel planes
    Koiso, M
    Palmer, B
    CALCULUS OF VARIATIONS AND PARTIAL DIFFERENTIAL EQUATIONS, 2006, 25 (03) : 275 - 298
  • [15] Stability of anisotropic capillary surfaces between two parallel planes
    Miyuki Koiso
    Bennett Palmer
    Calculus of Variations and Partial Differential Equations, 2006, 25 : 275 - 298
  • [16] An Implicit Method for Interpolating Two Digital Closed Curves on Parallel Planes
    Gabrielides, Nikolaos
    Cohen, Laurent
    SCALE SPACE AND VARIATIONAL METHODS IN COMPUTER VISION, PROCEEDINGS, 2009, 5567 : 672 - 683
  • [17] Surfaces of constant mean curvature bounded by two planar curves
    Lopez, R
    ANNALS OF GLOBAL ANALYSIS AND GEOMETRY, 1997, 15 (03) : 201 - 210
  • [18] Surfaces of Constant Mean Curvature Bounded by Two Planar Curves
    Rafael López
    Annals of Global Analysis and Geometry, 1997, 15 : 201 - 210
  • [19] Disks in Curves of Bounded Convex Curvature
    Aamand, Anders
    Abrahamsen, Mikkel
    Thorup, Mikkel
    AMERICAN MATHEMATICAL MONTHLY, 2020, 127 (07): : 579 - 593
  • [20] Minimal surfaces with the area growth of two planes: The case of infinite symmetry
    Meeks, William H., III
    Wolf, Michael
    JOURNAL OF THE AMERICAN MATHEMATICAL SOCIETY, 2007, 20 (02) : 441 - 465
12345