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math.SP2019
On principal frequencies, volume and inradius in convex sets
Lorenzo Brasco, Dario Mazzoleni
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…
math.SP2016
Spectral inequalities in quantitative form
Lorenzo Brasco, Guido De Philippis
We review some results about quantitative improvements of sharp inequalities for eigenvalues of the Laplacian.