On principal frequencies, volume and inradius in convex sets
arXiv:1911.08256
Abstract
We provide a sharp double-sided estimate for Poincaré-Sobolev constants on a convex set, in terms of its inradius and dimensional measure. Our results extend and unify previous works by Hersch and Protter (for the first eigenvalue) and of Makai, Pólya and Szegő (for the torsional rigidity), by means of a single proof.
23 pages, 3 figures