On weighted isoperimetric inequalities with non-radial densities

On weighted isoperimetric and Poincaré-type inequalities

Weighted isoperimetric and Poincaré-type inequalities are studied for κ-concave probability measures (in the hierarchy of convex measures).

On the Isoperimetric Problem for Radial Log-convex Densities

E e as balls centered at the origin, provided m ∈ [0, m0) for some (potentially computable) m0 > 0; this affirmatively answers conjecture [RCBM, Conjecture 3.12] for such values of the weighted volume parameter. We also prove that the set of weighted volumes such that this characterization holds true is open, thus reducing the proof of the full conjecture to excluding the possibility of bifurca...

Weighted Graph Laplacians and Isoperimetric Inequalities

We consider a weighted Cheeger’s constant for a graph and we examine the gap between the first two eigenvalues of Laplacian. We establish several isoperimetric inequalities concerning the unweighted Cheeger’s constant, weighted Cheeger’s constants and eigenvalues for Neumann and Dirichlet conditions .

Lp AFFINE ISOPERIMETRIC INEQUALITIES

Affine isoperimetric inequalities compare functionals, associated with convex (or more general) bodies, whose ratios are invariant under GL(n)-transformations of the bodies. These isoperimetric inequalities are more powerful than their better-known relatives of a Euclidean flavor. To be a bit more specific, this article deals with inequalities for centroid and projection bodies. Centroid bodies...

Isoperimetric Inequalities and Eigenvalues