Compact embedded minimal surfaces in the Berger sphere

Heayong Shin; Young Wook Kim; Sung-Eun Koh; Hyung Yong Lee; Seong-Deog Yang

doi:10.1016/j.crma.2018.01.011

Differential geometry

Compact embedded minimal surfaces in the Berger sphere
[Surfaces minimales compactes intégrées dans la sphère de Berger]

Présenté par : the Editorial Board

Heayong Shin ^1,² ; Young Wook Kim ³ ; Sung-Eun Koh ⁴ ; Hyung Yong Lee ³ ; Seong-Deog Yang ³

¹ Department of Mathematics, Chung-Ang University, Seoul 06974, Republic of Korea
² Department of Mathematics, KIAS, Seoul 20455, Republic of Korea
³ Department of Mathematics, Korea University, Seoul 02841, Republic of Korea
⁴ Department of Mathematics, Konkuk University, 05029, Republic of Korea

Comptes Rendus. Mathématique, Volume 356 (2018) no. 3, pp. 333-339.

complété par Addendum to the paper: Compact embedded minimal surfaces in the Berger sphere
[Addendum à l’article : Surfaces minimales compactes intégrées dans la sphère Berger]

Résumé
Abstract

Choe et Soret [1] ont construit une infinité de surfaces minimales compactes plongées dans $S^{3}$ en désingularisant deux tores de Clifford qui se rencontrent le long d'un grand cercle à un angle constant de la même taille. Nous montrons que leur méthode fonctionne également, avec quelques modifications, pour construire des surfaces minimales compactes plongées dans la sphère de Berger.

Choe and Soret [1] constructed infinitely many compact embedded minimal surfaces in $S^{3}$ by desingularizing Clifford tori which meet each other along a great circle at the angle of the same size. We show their method works with some modifications to construct compact embedded minimal surfaces in the Berger sphere as well.

Reçu le : 2017-06-09
Accepté le : 2018-01-23
Publié le : 2018-02-15

DOI : 10.1016/j.crma.2018.01.011

Affiliations des auteurs :

Heayong Shin ^{1, 2} ; Young Wook Kim ³ ; Sung-Eun Koh ⁴ ; Hyung Yong Lee ³ ; Seong-Deog Yang ³

¹ Department of Mathematics, Chung-Ang University, Seoul 06974, Republic of Korea
² Department of Mathematics, KIAS, Seoul 20455, Republic of Korea
³ Department of Mathematics, Korea University, Seoul 02841, Republic of Korea
⁴ Department of Mathematics, Konkuk University, 05029, Republic of Korea

@article{CRMATH_2018__356_3_333_0,
     author = {Heayong Shin and Young Wook Kim and Sung-Eun Koh and Hyung Yong Lee and Seong-Deog Yang},
     title = {Compact embedded minimal surfaces in the {Berger} sphere},
     journal = {Comptes Rendus. Math\'ematique},
     pages = {333--339},
     publisher = {Elsevier},
     volume = {356},
     number = {3},
     year = {2018},
     doi = {10.1016/j.crma.2018.01.011},
     language = {en},
}

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Heayong Shin; Young Wook Kim; Sung-Eun Koh; Hyung Yong Lee; Seong-Deog Yang. Compact embedded minimal surfaces in the Berger sphere. Comptes Rendus. Mathématique, Volume 356 (2018) no. 3, pp. 333-339. doi : 10.1016/j.crma.2018.01.011. https://comptes-rendus.academie-sciences.fr/mathematique/articles/10.1016/j.crma.2018.01.011/

Bibliographie
Cité par

[1] J. Choe; M. Soret New minimal surfaces in $S^{3}$ desingularizing the Clifford tori, Math. Ann., Volume 364 (2015), pp. 763-776

[2] H.B. Lawson Complete minimal surfaces in $S^{3}$ , Ann. of Math. (2), Volume 92 (1970), pp. 335-374

[3] W.W. Meeks; S.-T. Yau The existence of embedded minimal surfaces and the problem of uniqueness, Math. Z., Volume 179 (1982), pp. 151-168

[4] H. Shin; Y.W. Kim; S.-E. Koh; H.Y. Lee; S.-D. Yang Ruled minimal surfaces in the Berger sphere, Differ. Geom. Appl., Volume 40 (2015), pp. 209-222

[5] F. Torralbo Compact minimal surfaces in the Berger sphere, Ann. Glob. Anal. Geom., Volume 41 (2012), pp. 391-405

Cité par Sources :

^☆ In the memory of Professor Ok Kyung Yoon.

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