Il problema di Plateau in domini illimitati
Inégalité isopérimétrique et calibration
On montre que l’inégalité isopérimétrique pour un domaine dans le plan euclidien, la sphère de dimension 2, ou l’espace hyperbolique de dimension 2, peut s’obtenir à l’aide d’une calibration.
Integral functionals determined by their minima
Intégrandes normales et mesures paramétrées en calcul des variations
Inverse Function Theorems and Jacobians over Metric Spaces
We present inversion results for Lipschitz maps f : Ω ⊂ ℝN → (Y, d) and stability of inversion for uniformly convergent sequences. These results are based on the Area Formula and on the l.s.c. of metric Jacobians.
Isoperimetric and Stable Sets for Log-Concave Perturbations of Gaussian Measures
Let be an open half-space or slab in ℝn+1 endowed with a perturbation of the Gaussian measure of the form f (p) := exp(ω(p) − c|p|2), where c > 0 and ω is a smooth concave function depending only on the signed distance from the linear hyperplane parallel to ∂ Ω. In this work we follow a variational approach to show that half-spaces perpendicular to ∂ Ω uniquely minimize the weighted perimeter in Ω among sets enclosing the same weighted volume. The main ingredient of the proof is the characterization...
Isoperimetric inequalities for quermassintegrals