15 citations · 51 across the 14 of their papers we have counts for
15 papers
Sharp and rigid isoperimetric inequality in metric measure spaces with non-negative Ricci curvature
Bang-Xian Han
By using optimal transport theory, we prove a sharp dimension-free isoperimetric inequality involving the volume entropy, in metric measure spaces with non-negative Ricci curvature…
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.
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…
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…
Rigidity of some functional inequalities on RCD spaces
Bang-Xian Han
We study the cases of equality and prove a rigidity theorem concerning the 1-Bakry-Émery inequality. As an application, we prove the rigidity of the Gaussian isoperimetric inequali…
Curvature-dimension conditions for diffusions under time change
Bang-Xian Han, Karl-Theodor Sturm
We derive precise transformation formulas for synthetic lower Ricci bounds under time change. More precisely, for local Dirichlet forms we study how the curvature-dimension conditi…
The sharp -Poincaré inequality under the measure contraction property
Bang-Xian Han
We obtain sharp estimate on -spectral gaps, or equivalently optimal constant in -Poincaré inequalities, for metric measure spaces satisfying measure contraction property. We…
Sharp Poincaré inequalities under Measure Contraction Property
Bang-Xian Han, Emanuel Milman
We prove a sharp Poincaré inequality for subsets of (essentially non-branching) metric measure spaces satisfying the Measure Contraction Property , whose dia…
Measure rigidity of synthetic lower Ricci curvature bound on Riemannian manifolds
Bang-XIan Han
In this paper we investigate Lott-Sturm-Villani's synthetic lower Ricci curvature bound on Riemannian manifolds with boundary. We prove several measure rigidity results for some im…
Characterizations of monotonicity of vector fields on metric measure spaces
Bang-Xian Han
We characterize the convexity of functions and the monotonicity of vector fields on metric measure spaces with Riemannian Ricci curvature bounded from below. Our result offers a ne…
Ricci tensor on smooth metric measure space with boundary
Bang-Xian Han
The aim of this note is to study the measure-valued Ricci tensor on smooth metric measure space with boundary, which is a generalization of Bakry-Emery's modified Ricci tensor on w…
New characterizations of Ricci curvature on RCD metric measure spaces
Bang-Xian Han
We prove that on a large family of metric measure spaces, if the -gradient estimate for heat flows holds for some , then the -gradient estimate also holds. This resu…
Angles between curves in metric measure spaces
Bang-Xian Han, Andrea Mondino
The goal of the paper is to study the angle between two curves in the framework of metric (and metric measure) spaces. More precisely, we give a new notion of angle between two cur…
Sobolev spaces on warped products
Nicola Gigli, Bang-Xian Han
We study the structure of Sobolev spaces on the cartesian/warped products of a given metric measure space and an interval. Our main results are: - the characterization of the Sobol…
Conformal transformation on metric measure spaces
Bang-Xian Han
We study several problems concerning conformal transformation on metric measure spaces, including the Sobolev space, the differential structure and the curvature-dimension conditio…