Mean curvature 1 surfaces in hyperbolic 3-space with low total curvature I

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dc.creatorRossman, Wayne
dc.creatorUmehara, Masaaki
dc.creatorYamada, Kotaro
dc.date2000-08-02
dc.date.accessioned2026-07-07T09:35:21Z
dc.date.available2026-07-07T09:35:21Z
dc.descriptionA complete surface of constant mean curvature 1 (CMC-1) in hyperbolic 3-space with constant curvature -1 has two natural notions of "total curvature"-- one is the total absolute curvature which is the integral over the surface of the absolute value of the Gaussian curvature, and the other is the dual total absolute curvature which is the total absolute curvature of the dual CMC-1 surface. In this paper, we completely classify CMC-1 surfaces with dual total absolute curvature at most 4π. Moreover, we give new examples and partially classify CMC-1 surfaces with dual total absolute curvature at most 8π.
dc.description28pages, 5 figures
dc.identifierhttps://arxiv.org/abs/math/0008015
dc.identifierhttp://arxiv.org/abs/math/0008015
dc.identifierHiroshima Math. J. 34 (2004), 21-56
dc.identifier.urihttp://salesiana.dossiersoluciones.com/handle/123456789/159807
dc.subjectDifferential Geometry
dc.subject53A10; 53A35; 53A42
dc.titleMean curvature 1 surfaces in hyperbolic 3-space with low total curvature I
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