Regularity of volume-minimizing flows on 3-manifolds

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dc.creatorJohnson, David L.
dc.creatorSmith, Penelope
dc.date2005-05-12
dc.date.accessioned2026-07-07T05:19:52Z
dc.date.available2026-07-07T05:19:52Z
dc.descriptionIn this article, we show that, for any compact 3-manifold, there is a $C^{1}$ volume-minimizing one-dimensional foliation. More generally, we show the existence of mass-minimizing rectifiable sections of sphere bundles without isolated "pole points" in the base manifold. This same analysis is used to show that the examples, due to Sharon Pedersen, of potentially volume-minimizing rectifiable sections (rectifiable foliations) of the unit tangent bundle to $S^{2n+1}$ are not, in fact, volume minimizing.
dc.description11 pages, no figures, LaTeX
dc.identifierhttps://arxiv.org/abs/math/0505263
dc.identifierhttp://arxiv.org/abs/math/0505263
dc.identifier.urihttp://salesiana.dossiersoluciones.com/handle/123456789/75180
dc.subjectDifferential Geometry
dc.subjectAnalysis of PDEs
dc.subject49F20, 49F22, 49F10, 58A25, 53C42, 53C65
dc.titleRegularity of volume-minimizing flows on 3-manifolds
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