On the isoperimetric profile for a mixed Euclidean–Log-convex measure

Abstract

We study the isoperimetric problem in ${\mathbb{R}}^h\times {\mathbb{R}}^k$ endowed with a mixed Euclidean–Log-convex measure $\lambda =e^{\psi (x)}dxdy$. We prove the existence of an isoperimetric set and we show some of its qualitative properties.