On the Index of Minimal Surfaces with Free Boundary in a Half-Space

被引：0
作者：
Shuli Chen
机构：
[1] Stanford University,Department of Mathematics
来源：
The Journal of Geometric Analysis | 2023年 / 33卷
关键词：
Minimal surfaces; Morse index; Free boundary; 53A10;
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学科分类号：
摘要：
We study the Morse index of minimal surfaces with free boundary in a half-space. We improve previous estimates relating the Neumann index to the Dirichlet index and use this to answer a question of Ambrozio, Buzano, Carlotto, and Sharp concerning the non-existence of index two embedded minimal surfaces with free boundary in a half-space. We also give a simplified proof of a result of Chodosh and Maximo concerning lower bounds for the index of the Costa deformation family.
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[1]  
Fischer-Colbrie D(1985)On complete minimal surfaces with finite Morse index in three manifolds Invent. Math. 82 121-132
[2]  
Gulliver R(1986)The structure of stable minimal hypersurfaces near a singularity Proc. Symp. Pure Math. 44 213-237
[3]  
Lawson HB(1986)Index and total curvature of complete minimal surfaces Proc. Symp. Pure Math. 44 207-211
[4]  
Gulliver R(1980)The structure of complete stable minimal surfaces in 3-manifolds of non-negative scalar curvature Commun. Pure Appl. Math. 33 199-211
[5]  
Fischer-Colbrie D(1979)Stable complete minimal surfaces in Bull. Am. Math. Soc. 1 903-906
[6]  
Schoen R(1981) are planes Doklady Akad. Nauk 260 293-295
[7]  
do Carmo M(1989)On the stability of minimal surfaces Comment. Math. Helvet. 64 34-43
[8]  
Peng C-K(2016)Complete minimal surfaces with index one and stable constant mean curvature surfaces J. Differ. Geom. 104 399-418
[9]  
Pogorelov AV(2018)On the topology and index of minimal surfaces Cal. Var. Partial Differ. Equ. 57 22-664
[10]  
López FJ(2019)Compactness analysis for free boundary minimal hypersurfaces J. l’Écol. Polytech. Math. 6 621-405
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