Mean Convex Hulls and Least Area Disks spanning Extreme Curves

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dc.creatorCoskunuzer, Baris
dc.date2004-12-29
dc.date2005-06-06
dc.date.accessioned2026-07-07T06:28:50Z
dc.date.available2026-07-07T06:28:50Z
dc.descriptionWe show that for any extreme curve in a 3-manifold M, there exist a canonical mean convex hull containing all least area disks spanning the curve. Similar result is true for asymptotic case in hyperbolic 3-space such that for any asymptotic curve, there is a canonical mean convex hull containing all minimal planes spanning that curve. Applying this to quasi-Fuchsian manifolds, we show that for any quasi-Fuchsian manifold, there exist a canonical mean convex core capturing all essential minimal surfaces. On the other hand, we also show that for a generic C^3-smooth curve in the boundary of C^3-smooth mean convex domain in R^3, there exist a unique least area disk spanning the curve.
dc.description18 pages
dc.identifierhttps://arxiv.org/abs/math/0412529
dc.identifierhttp://arxiv.org/abs/math/0412529
dc.identifierMath Z. 252 (2006) 811--824
dc.identifier.urihttp://salesiana.dossiersoluciones.com/handle/123456789/97836
dc.subjectDifferential Geometry
dc.subjectGeometric Topology
dc.subject53A10 ; 57N10
dc.titleMean Convex Hulls and Least Area Disks spanning Extreme Curves
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