A combinatorial curvature flow for compact 3-manifolds with boundary

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dc.creatorLuo, Feng
dc.date2004-05-14
dc.date2004-05-16
dc.date.accessioned2026-07-07T05:08:17Z
dc.date.available2026-07-07T05:08:17Z
dc.descriptionWe introduce a combinatorial curvature flow for PL metrics on compact triangulated 3-manifolds with boundary consisting of surfaces of negative Euler characteristic. The flow tends to find the complete hyperbolic metric with totally geodesic boundary on a manifold. Some of the basic properties of the combinatorial flow are established. The most important ones is that the evolution of the PL curvature satisfies a combinatorial heat equation. It implies that the total curvature decreases along the flow. The local convergence of the flow to the hyperbolic metric is also established if the triangulation is isotopic to a totally geodesic triangulation.
dc.description6 pages, 1 firure
dc.identifierhttps://arxiv.org/abs/math/0405295
dc.identifierhttp://arxiv.org/abs/math/0405295
dc.identifierelectronic research announcements, AMS, Volume 11, Pages 12--20 (January 28, 2005)
dc.identifier.urihttp://salesiana.dossiersoluciones.com/handle/123456789/71203
dc.subjectGeometric Topology
dc.subjectDifferential Geometry
dc.subject53C44, 52A55
dc.titleA combinatorial curvature flow for compact 3-manifolds with boundary
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