Nonlinear evolution by mean curvature and isoperimetric inequalities

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dc.creatorSchulze, Felix
dc.date2006-06-27
dc.date.accessioned2026-07-07T07:17:43Z
dc.date.available2026-07-07T07:17:43Z
dc.descriptionEvolving smooth, compact hypersurfaces in R^{n+1} with normal speed equal to a positive power k of the mean curvature improves a certain 'isoperimetric difference' for k >= n-1. As singularities may develop before the volume goes to zero, we develop a weak level-set formulation for such flows and show that the above monotonicity is still valid. This proves the isoperimetric inequality for n <= 7. Extending this to complete, simply connected 3-dimensional manifolds with nonpositive sectional curvature, we give a new proof for the Euclidean isoperimetric inequality on such manifolds.
dc.description42 pages
dc.identifierhttps://arxiv.org/abs/math/0606675
dc.identifierhttp://arxiv.org/abs/math/0606675
dc.identifier.urihttp://salesiana.dossiersoluciones.com/handle/123456789/114042
dc.subjectDifferential Geometry
dc.subjectAnalysis of PDEs
dc.subject28A75; 49Q20; 53C44
dc.titleNonlinear evolution by mean curvature and isoperimetric inequalities
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