-energy of a curve on LIP-manifolds and on general metric spaces.
Perimeter on Fractal sets.
Phase field method for mean curvature flow with boundary constraints
This paper is concerned with the numerical approximation of mean curvature flow t → Ω(t) satisfying an additional inclusion-exclusion constraint Ω1 ⊂ Ω(t) ⊂ Ω2. Classical phase field model to approximate these evolving interfaces consists in solving the Allen-Cahn equation with Dirichlet boundary conditions. In this work, we introduce a new phase field model, which can be viewed as an Allen Cahn equation with a penalized double well potential. We first justify this method by a Γ-convergence result...
Phase field method for mean curvature flow with boundary constraints
This paper is concerned with the numerical approximation of mean curvature flow t → Ω(t) satisfying an additional inclusion-exclusion constraint Ω1 ⊂ Ω(t) ⊂ Ω2. Classical phase field model to approximate these evolving interfaces consists in solving the Allen-Cahn equation with Dirichlet boundary conditions. In this work, we introduce a new phase field model, which can be viewed as an Allen Cahn equation with a penalized double well potential. We first justify this method by a Γ-convergence result...
Plongements quasiisométriques du groupe de Heisenberg dans , d’après Cheeger, Kleiner, Lee, Naor
Bref survol du théorème de non-plongement de J. Cheeger et B. Kleiner pour le groupe d’Heisenberg dans .