Complete bounded holomorphic curves immersed in C^2 with arbitrary genus

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dc.creatorMartin, Francisco
dc.creatorUmehara, Masaaki
dc.creatorYamada, Kotaro
dc.date2008-10-29
dc.date.accessioned2026-07-07T10:13:51Z
dc.date.available2026-07-07T10:13:51Z
dc.descriptionIn the previous paper, the authors constructed a complete holomorphic immersion of the unit disk D into C^2 whose image is bounded. In this paper, we shall prove existence of complete holomorphic null immersions of Riemann surfaces with arbitrary genus and finite topology, whose image is bounded in C^2. To construct such immersions, we apply the method used by F. J. Lopez to perturb the genus zero example changing its genus. As an analogue the above construction, we also give a new method to construct complete bounded minimal immersions (resp. weakly complete maximal surface) with arbitrary genus and finite topology in Euclidean 3-space (resp. Lorentz-Minkowski 3-spacetime).
dc.description12 pages, 1 figure
dc.identifierhttps://arxiv.org/abs/0810.5193
dc.identifierhttp://arxiv.org/abs/0810.5193
dc.identifier.urihttp://salesiana.dossiersoluciones.com/handle/123456789/172676
dc.subjectDifferential Geometry
dc.subject53A10; 49Q05
dc.titleComplete bounded holomorphic curves immersed in C^2 with arbitrary genus
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