no. G1
Géométrie et Topologie
Addendum to the paper: Compact embedded minimal surfaces in the Berger sphere
[Addendum à l’article : Surfaces minimales compactes intégrées dans la sphère Berger]
Shin, Heayong1 ; Kim, Young Wook2 ; Koh, Sung-Eun3  ; Lee, Hyung Yong2 ; Yang, Seong-Deog2
1Department of Mathematics, Chung-Ang University, Seoul 06974, Korea
2Department of Mathematics, Korea University, Seoul 02841, Korea
3Department of Mathematics, Konkuk University, Seoul 05029, Korea
Comptes Rendus. Mathématique, Tome 361 (2023) no. G1, pp. 257-264
complète Compact embedded minimal surfaces in the Berger sphere
[Surfaces minimales compactes intégrées dans la sphère de Berger]

We construct a two discrete parameter family of compact minimal surfaces embedded in the Berger sphere which may be considered as the analogue of the helicoidal Karcher-Scherk surfaces.

Nous construisons une famille à deux paramètres discrets de surfaces minimales compactes plongées dans la sphère de Berger qui peut être considérée comme l’analogue de l’hélicoïde de Karcher-Scherk.

Reçu le :
Révisé le :
Accepté le :
Publié le :
DOI : 10.5802/crmath.403

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

1 Department of Mathematics, Chung-Ang University, Seoul 06974, Korea
2 Department of Mathematics, Korea University, Seoul 02841, Korea
3 Department of Mathematics, Konkuk University, Seoul 05029, Korea
Licence : CC-BY 4.0
Droits d'auteur : Les auteurs conservent leurs droits
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     author = {Shin, Heayong and Kim, Young Wook and Koh, Sung-Eun and Lee, Hyung Yong and Yang, Seong-Deog},
     title = {Addendum to the paper: {Compact} embedded minimal surfaces in the {Berger} sphere},
     journal = {Comptes Rendus. Math\'ematique},
     pages = {257--264},
     year = {2023},
     publisher = {Acad\'emie des sciences, Paris},
     volume = {361},
     number = {G1},
     doi = {10.5802/crmath.403},
     language = {en},
     url = {https://numdam.org/articles/10.5802/crmath.403/}
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Shin, Heayong; Kim, Young Wook; Koh, Sung-Eun; Lee, Hyung Yong; Yang, Seong-Deog. Addendum to the paper: Compact embedded minimal surfaces in the Berger sphere. Comptes Rendus. Mathématique, Tome 361 (2023) no. G1, pp. 257-264. doi: 10.5802/crmath.403

[1] (https://minimalsurfaces.blog/home/repository/singly-periodic/ helicoidal-karcher-scherk-surfaces/)

[2] Meeks, III William H.; Yau, Shing-Tung The existence of embedded minimal surfaces and the problem of uniqueness, Math. Z., Volume 179 (1982), pp. 151-168 | DOI | MR | Zbl

[3] Shin, Heayong; Kim, Young Wook; Koh, Sung-Eun; Lee, Hyung Yong; Yang, Seong-Deog Ruled minimal surfaces in the Berger sphere, Differ. Geom. Appl., Volume 40 (2015), pp. 209-222 | DOI | MR | Zbl

[4] Shin, Heayong; Kim, Young Wook; Koh, Sung-Eun; Lee, Hyung Yong; Yang, Seong-Deog Compact embedded minimal surfaces in the Berger sphere, C. R. Acad. Sci. Paris, Volume 356 (2018) no. 3, pp. 333-339 | DOI | MR | Zbl

[5] Shin, Heayong; Kim, Young Wook; Koh, Sung-Eun; Lee, Hyung Yong; Yang, Seong-Deog Schwarz’ CLP-surfaces in Nil 3 , Proc. Am. Math. Soc., Volume 147 (2019) no. 4, pp. 1677-1685 | DOI | Zbl

[6] Torralbo, Francisco Compact minimal surfaces in the Berger spheres, Ann. Global Anal. Geom., Volume 41 (2012) no. 4, pp. 391-405 | DOI | MR | Zbl

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