Complete surfaces with positive extrinsic curvature in product spaces

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dc.creatorEspinar, Jose M.
dc.creatorGalvez, Jose A.
dc.creatorRosenberg, Harold
dc.date2007-05-04
dc.date2007-05-09
dc.date.accessioned2026-07-07T07:59:55Z
dc.date.available2026-07-07T07:59:55Z
dc.descriptionWe prove that every complete connected immersed surface with positive extrinsic curvature $K$ in $H^2\times R$ must be properly embedded, homeomorphic to a sphere or a plane and, in the latter case, study the behavior of the end. Then, we focus our attention on surfaces with positive constant extrinsic curvature ($K-$surfaces). We establish that the only complete $K-$surfaces in $S^2\times R$ and $H^2\times R$ are rotational spheres. Here are the key steps to achieve this. First height estimates for compact $K-$surfaces in a general ambient space $M^2\times R$ with boundary in a slice are obtained. Then distance estimates for compact $K-$surfaces (and H-$surfaces) in $H^2\times R$ with boundary on a vertical plane are obtained. Finally we construct a quadratic form with isolated zeroes of negative index.
dc.description28 pages
dc.identifierhttps://arxiv.org/abs/0705.0585
dc.identifierhttp://arxiv.org/abs/0705.0585
dc.identifier.urihttp://salesiana.dossiersoluciones.com/handle/123456789/128547
dc.subjectDifferential Geometry
dc.titleComplete surfaces with positive extrinsic curvature in product spaces
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