17 jun 2014 -- 16:30 [open in google calendar]
In a recent paper X. Cabre’, X. Ros and J. Serra obtain a new family of sharp isoperimetric inequalities with weights in open convex cones of Rn. They prove that, under some concavity conditions on the weight, Euclidean balls centered at the origin (intersected with the cone) minimize the weighted isoperimetric quotient, even if the weights are nonradial —except for the constant ones. Their proof is based on the ABP method applied to an appropriate linear Neumann problem. In this talk I will present the quantitative version of these isoperimetric inequelities, whose proof is still based on the ABP method, combined with some weigthed trace inequality which allows to 1 obtain the optimal exponent on the isoperimetric deficit. This is a joint work with X. Cabre’, A. Pratelli, X. Ros and J. Serra.