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math.MG2021
A sharp isoperimetric inequality in metric measure spaces with non-negative Ricci curvature
Bang-Xian Han
We prove a sharp dimension-free isoperimetric inequality, involving the volume entropy, in non-compact metric measure spaces with non-negative synthetic Ricci curvature.
math.FA2021★ 4 cited
On the asymptotic behaviour of the fractional Sobolev seminorms in metric measure spaces: Bourgain-Brezis-Mironescu's theorem revisited
Bang-Xian Han, Andrea Pinamonti
We generalize Bourgain-Brezis-Mironescu's asymptotic formula for fractional Sobolev functions, in the setting of abstract metric measure spaces, under the assumption that at almost…
math.FA2021★ 1 cited
On the asymptotic behaviour of the fractional Sobolev seminorms in metric measure spaces: asymptotic volume ratio, volume entropy and rigidity
Bang-Xian Han, Andrea Pinamonti
We study the asymptotic behaviour of suitably defined seminorms in general metric measure spaces. As a particular case we provide new and shorter proofs of the Maz'ya-Shaposhnikova…