Let Ω⊂ R d be an open set, and consider the Laplacian operator−∆ on Ω under various
boundary conditions. When the relevant spectrum happens to be discrete, it is an interesting …

We completely characterize isoperimetric regions in Rn with density eh, where h is convex,
smooth, and radially symmetric. In particular, balls around the origin constitute isoperimetric …

We solve a class of isoperimetric problems on RN with respect to weights that are powers of
the distance to the origin. For instance we show that, if k∈[0, 1], then among all smooth sets …

We consider the problem of minimizing the first non-trivial Stekloff eigenvalue of the
Laplacian, among sets with given measure. We prove that the Brock–Weinstock inequality …

Given a smooth, radial, uniformly log-convex density e V on R^ n, n≥ 2, we characterize
isoperimetric sets E with respect to weighted perimeter ∂ E e^ V d H^ n-1 and weighted …

According to a celebrated result of L. Caffarelli, every optimal mass transportation mapping
pushing forward the standard Gaussian measure onto a log-concave measure $ e^{-W} dx …

The isoperimetric problem with respect to the product-type density [Formula: see text] on the
Euclidean space Rh× Rk is studied. In particular, existence, symmetry and regularity of …

We solve a class of isoperimetric problems on with respect to monomial weights. Let α and β
be real numbers such that 0≤ α< β+ 1, β≤ 2α. We show that, among all smooth sets Ω in …

A weighted relative isoperimetric inequality in convex cones is obtained via the Monge-
Ampere equation. The method improves several inequalities in the literature, eg constants in …

We examine the vertical component of surface area in the warped product of a Euclidean
interval and a fiber manifold with product density. We determine general conditions under …