no. G10
Géométrie et Topologie
Genus Zero Complete Maximal Maps and Maxfaces with an Arbitrary Number of Ends
Kumar, Pradip1  ; Mohanty, Sai Rasmi Ranjan1
1 Department of Mathematics, Shiv Nadar Institute of Eminence, Deemed to be University, Dadri 201314, Uttar Pradesh, India
Comptes Rendus. Mathématique, Tome 361 (2023) no. G10, pp. 1683-1690

We prove the existence of a genus-zero complete maximal map with a prescribed singularity set and an arbitrary number of simple and complete ends. We also discuss the conditions under which this maximal map can be made into a complete maxface.

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Révisé le :
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DOI : 10.5802/crmath.525
Classification : 53A35
Keywords: complete maxface, maximal map, zero mean curvature surfaces

Kumar, Pradip 1 ; Mohanty, Sai Rasmi Ranjan 1

1 Department of Mathematics, Shiv Nadar Institute of Eminence, Deemed to be University, Dadri 201314, Uttar Pradesh, India
Licence : CC-BY 4.0
Droits d'auteur : Les auteurs conservent leurs droits 
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     title = {Genus {Zero} {Complete} {Maximal} {Maps} and {Maxfaces} with an {Arbitrary} {Number} of {Ends}},
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Kumar, Pradip; Mohanty, Sai Rasmi Ranjan. Genus Zero Complete Maximal Maps and Maxfaces with an Arbitrary Number of Ends. Comptes Rendus. Mathématique, Tome 361 (2023) no. G10, pp. 1683-1690. doi: 10.5802/crmath.525

[1] Estudillo, Francisco J. M.; Romero, Alfonso Generalized maximal surfaces in Lorentz–Minkowski space 𝕃 3 , Math. Proc. Camb. Philos. Soc., Volume 111 (1992) no. 3, pp. 515-524 | DOI | Zbl | MR

[2] Fujimori, Shoichi; Rossman, Wayne; Umehara, Masaaki; Yamada, Kotaro; Yang, Seong-Deog New Maximal Surfaces in Minkowski 3-Space with Arbitrary Genus and Their Cousins in de Sitter 3-Space, Results Math., Volume 56 (2009) no. 1, p. 41 | DOI | MR | Zbl

[3] Gronwall, Thomas H. On analytic functions of constant modulus on a given contour, Ann. Math., Volume 14 (1912) no. 1-4, pp. 72-80 | DOI | MR

[4] Imaizumi, Taishi; Kato, Shin Flux of simple ends of maximal surfaces in ℝ 2,1 , Hokkaido Math. J., Volume 37 (2008) no. 3, pp. 561-610 | DOI | MR | Zbl

[5] Jorge, Luquésio P.; Meeks, William H. III The topology of complete minimal surfaces of finite total Gaussian curvature, Topology, Volume 22 (1983) no. 2, pp. 203-221 | DOI | MR | Zbl

[6] Kim, Young Wook; Yang, Seong-Deog Prescribing singularities of maximal surfaces via a singular Björling representation formula, J. Geom. Phys., Volume 57 (2007) no. 11, pp. 2167-2177 | DOI | Zbl

[7] López, Rafael On the existence of spacelike constant mean curvature surfaces spanning two circular contours in Minkowski space, J. Geom. Phys., Volume 57 (2007) no. 11, pp. 2178-2186 | DOI | MR | Zbl

[8] Naoya, Ando; Kohei, Hamada; Kaname, Hasimoto; Shin, Kato Regularity of ends of zero mean curvature surfaces in ℝ 2,1 , J. Math. Soc. Japan, Volume 74 (2022) no. 4, pp. 1295-1334 | DOI | MR | Zbl

[9] Osgood, Brad Old and New on the Schwarzian Derivative, Quasiconformal Mappings and Analysis: A Collection of Papers Honoring F.W. Gehring (Duren, Peter; Heinonen, Juha; Osgood, Brad; Palka, Bruce, eds.), Springer, 1998, pp. 275-308 | DOI | Zbl

[10] Umehara, Masaaki; Yamada, Kotaro Maximal surfaces with singularities in Minkowski space, Hokkaido Math. J., Volume 35 (2006) no. 1, pp. 13-40 | DOI | MR | Zbl

[11] Yang, Kichoon Complete minimal surfaces of finite total curvature, Mathematics and its Applications, 294, Kluwer Academic Publishers, 1994, viii+157 pages | DOI | MR

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