Orateur
Prof.
Frank Pacard
(Ecole polytechnique)
Description
There is a strong parallel between the theory of minimal hypersurfaces and the solutions of the double-well phase transition Allen-Cahn equation on a manifold. In this talk, I will report some recent result on the relations between geodesics on surfaces and solutions of the Allen-Cahn equation with uniform bounds on the Morse Index and energy, as the phase transition parameter tends to 0. Our results show that the situation in 2-dimensions is strikingly different from the situation in dimension 3 and higher. This is a joint work with Juncheng Wei and Yong Liu.
Auteur principal
Prof.
Frank Pacard
(Ecole polytechnique)
