no. 3
Differential geometry
Compact embedded minimal surfaces in the Berger sphere
[Surfaces minimales compactes intégrées dans la sphère de Berger]

Présenté par : the Editorial Board

Shin, Heayong1, 2 ; Kim, Young Wook3 ; Koh, Sung-Eun4 ; Lee, Hyung Yong3 ; Yang, Seong-Deog3
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, Tome 356 (2018) no. 3, pp. 333-339.

Choe et Soret [1] ont construit une infinité de surfaces minimales compactes plongées dans S3 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 S3 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 :
Accepté le :
Publié le :
DOI : 10.1016/j.crma.2018.01.011
Shin, Heayong 1, 2 ; Kim, Young Wook 3 ; Koh, Sung-Eun 4 ; Lee, Hyung Yong 3 ; Yang, Seong-Deog 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 
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Shin, Heayong; Kim, Young Wook; Koh, Sung-Eun; Lee, Hyung Yong; Yang, Seong-Deog. Compact embedded minimal surfaces in the Berger sphere. Comptes Rendus. Mathématique, Tome 356 (2018) no. 3, pp. 333-339. doi : 10.1016/j.crma.2018.01.011. http://archive.numdam.org/articles/10.1016/j.crma.2018.01.011/

[1] Choe, J.; Soret, M. New minimal surfaces in S3 desingularizing the Clifford tori, Math. Ann., Volume 364 (2015), pp. 763-776

[2] Lawson, H.B. Jr. Complete minimal surfaces in S3, Ann. of Math. (2), Volume 92 (1970), pp. 335-374

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

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

[5] Torralbo, F. 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.