First Eigenvalue of Symmetric Minimal Surfaces in S3

被引：15

作者：

Choe, Jaigyoung ^{[1
]}

Soret, Marc ^{[2
]}

机构：

[1] Korea Inst Adv Study, Seoul 130722, South Korea

[2] Univ E Rabelais, Dept Math, F-37200 Tours, France

来源：

INDIANA UNIVERSITY MATHEMATICS JOURNAL | 2009年 / 58卷 / 01期

关键词：

Laplacian; eigenvalue; minimal surface; S3;

D O I：

10.1512/iumj.2009.58.3192

中图分类号：

O1 [数学];

学科分类号：

0701 ; 070101 ;

摘要：

Let lambda(1) be the first nontrivial eigenvalue of the Laplacian on a compact surface without boundary. We show that lambda(1) = 2 on compact embedded minimal surfaces in S-3 which are invariant under a finite group of reflections-and whose fundamental piece is simply connected and has less than six edges, In particular lambda(1) = 2 on compact embedded minimal surfaces in S-3 that are constructed by Lawson and by Karcher-Pinkall-Sterling.

引用

页码：269 / 281

页数：13

共 50 条

[11] QUADRIC REPRESENTATION OF MINIMAL-SURFACES OF S3
BARROS, M
GARAY, OJ
COMPTES RENDUS DE L ACADEMIE DES SCIENCES SERIE I-MATHEMATIQUE, 1994, 319 (02): : 175 - 179
[12] Minimal surfaces in S3: a survey of recent results
Brendle, Simon
BULLETIN OF MATHEMATICAL SCIENCES, 2013, 3 (01) : 133 - 171
[13] Minimal surfaces in S3 with constant contact angle
Montes, Rodrigo Ristow
Verderesi, Jose A.
MONATSHEFTE FUR MATHEMATIK, 2009, 157 (04): : 379 - 386
[14] Minimal surfaces in S3 with constant contact angle
Rodrigo Ristow Montes
Jose A. Verderesi
Monatshefte für Mathematik, 2009, 157 : 379 - 386
[15] DPW potentials for compact symmetric CMC surfaces in S3
Manca, Benedetto
JOURNAL OF GEOMETRY AND PHYSICS, 2020, 156
[16] Characterization of order 3 algebraic immersed minimal surfaces of S3
Perdomo, Oscar Mario
GEOMETRIAE DEDICATA, 2007, 129 (01) : 23 - 34
[17] Characterization of order 3 algebraic immersed minimal surfaces of S3
Oscar Mario Perdomo
Geometriae Dedicata, 2007, 129 : 23 - 34
[18] MINIMAL LEGENDRIAN SURFACES IN THE TANGENT SPHERE BUNDLE OF S3
Li, Mingyan
Wang, Yanan
PROCEEDINGS OF THE AMERICAN MATHEMATICAL SOCIETY, 2024, 152 (05) : 2205 - 2220
[19] New minimal surfaces in S3 desingularizing the Clifford tori
Choe, Jaigyoung
Soret, Marc
MATHEMATISCHE ANNALEN, 2016, 364 (3-4) : 763 - 776
[20] AN EXTRINSIC RIGIDITY THEOREM FOR MINIMAL-SURFACES IN S3
LI, AM
MATHEMATISCHE ZEITSCHRIFT, 1985, 190 (02) : 221 - 224

← 1 2 3 4 5 →