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

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 ≥ 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.