Strong minimizers of Blake & Zisserman functional
On montre que, sur une surface riemannienne compacte, le profil isopérimétrique admet un développement limité à l’ordre en . Lorsque la métrique est analytique, le profil est semi-analytique. Il existe des métriques lisses sur la -sphère dont le profil n’est pas de classe au voisinage de .
The irrigation problem is the problem of finding an efficient way to transport a measure μ+ onto a measure μ-. By efficient, we mean that a structure that achieves the transport (which, following [Bernot, Caselles and Morel, Publ. Mat.49 (2005) 417–451], we call traffic plan) is better if it carries the mass in a grouped way rather than in a separate way. This is formalized by considering costs functionals that favorize this property. The aim of this paper is to introduce a dynamical cost functional...