A measure theoretic approach to higher codimension mean curvature flows

Luigi Ambrosio; Halil Mete Soner

Displaying similar documents to “A measure theoretic approach to higher codimension mean curvature flows”

Mean curvature of a measure and related variational problems

Guy Bouchitté, Giuseppe Buttazzo, Ilaria Fragalà (1997)

Annali della Scuola Normale Superiore di Pisa - Classe di Scienze

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Vortex filament dynamics for Gross-Pitaevsky type equations

Robert L. Jerrard (2002)

Annali della Scuola Normale Superiore di Pisa - Classe di Scienze

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We study solutions of the Gross-Pitaevsky equation and similar equations in $m \geq 3$ space dimensions in a certain scaling limit, with initial data $u_{0}^{ϵ}$ for which the jacobian $J u_{0}^{ϵ}$ concentrates around an (oriented) rectifiable $m - 2$ dimensional set, say $Γ_{0}$ , of finite measure. It is widely conjectured that under these conditions, the jacobian at later times $t > 0$ continues to concentrate around some codimension $2$ submanifold, say $Γ_{t}$ , and that the family ${Γ_{t}}$ of submanifolds evolves by binormal mean curvature flow....

Some remarks on the continuity equation

Patrick Bernard (2008-2009)

Séminaire Équations aux dérivées partielles

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This text is the act of a talk given november 18 2008 at the seminar PDE of Ecole Polytechnique. The text is not completely faithfull to the oral exposition for I have taken this opportunity to present the proofs of some results that are not easy to find in the literature. On the other hand, I have been less precise on the material for which I found good references. Most of the novelties presented here come from a joined work with Luigi Ambrosio.