Geodesic
Proper superminimal surfaces of given conformal types in the hyperbolic four-space
Forstnerič, Franc1
1 Faculty of Mathematics and Physics, University of Ljubljana, Jadranska 19, SI–1000 Ljubljana, Slovenia, and, Institute of Mathematics, Physics and Mechanics, Jadranska 19, SI–1000 Ljubljana, Slovenia
Annales de la Faculté des sciences de Toulouse : Mathématiques, Série 6, Tome 32 (2023) no. 1, pp. 145-172

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Let H 4 denote the hyperbolic four-space. Given a bordered Riemann surface, M, we prove that every smooth conformal superminimal immersion M ¯→H 4 can be approximated uniformly on compacts in M by proper conformal superminimal immersions M→H 4 . In particular, H 4 contains properly immersed conformal superminimal surfaces normalised by any given open Riemann surface of finite topological type without punctures. The proof uses the analysis of holomorphic Legendrian curves in the twistor space of H 4 .

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DOI : 10.5802/afst.1732
Classification : 53A10, 53C28, 32E30, 37J55
Keywords: superminimal surface, hyperbolic space, twistor space, complex contact manifold, holomorphic Legendrian curve

Forstnerič, Franc 1

1 Faculty of Mathematics and Physics, University of Ljubljana, Jadranska 19, SI–1000 Ljubljana, Slovenia, and, Institute of Mathematics, Physics and Mechanics, Jadranska 19, SI–1000 Ljubljana, Slovenia
Licence : CC-BY 4.0
Droits d'auteur : Les auteurs conservent leurs droits 
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     title = {Proper superminimal surfaces of given conformal types in the hyperbolic four-space},
     journal = {Annales de la Facult\'e des sciences de Toulouse : Math\'ematiques},
     pages = {145--172},
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Forstnerič, Franc. Proper superminimal surfaces of given conformal types in the hyperbolic four-space. Annales de la Faculté des sciences de Toulouse : Mathématiques, Série 6, Tome 32 (2023) no. 1, pp. 145-172. doi: 10.5802/afst.1732

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