My Research
Research interest
My research is focused on optimal transport and its applications on functional inequalities, metric measure spaces etc., I am interested in mathematics objects related to both metrics and measures.
In particular, I have worked mainly on the following topics:
1. optimal transport, analysis and geometry of Wasserstein space
2. metric measure space with synthetic Ricci curvature bound
3. Sobolev space on metric measure space
4. Bakry-Emery's theory, geometric and functional inequalities
Publications & Preprints
0. (Ph.D thesis) Topics on calculus on metric measure spaces，defense on 23 June 2015 at Paris, thesis-on-line: archives-ouvertes
1. (with N. Gigli) The continuity equation on metric measure spaces, Cal.Var.PDE. (2015), preprint at: arxiv.
2. (with N. Gigli) Independence on p of weak upper gradients on RCD spaces, J.Funct. Anal. (2016), preprint at: arxiv.
3. (with A. Mondino) Angles between curves in metric measure spaces, Anal. Geom. Metr. Spaces. (2017), preprint at: arxiv.
4. Ricci tensor on RCD(K,N) space, J. Geom. Anal. (2018), preprint at: arxiv.
5. (with N. Gigli) Sobolev Spaces on Warped Products, J. Funct. Anal. (2018), preprint at: arxiv.
6. Conformal transformation on metric measure spaces, Potential.Anal. (2019), preprint at: arxiv.
7. New characterizations of Ricci curvature on RCD metric measure spaces, Disc. Cont. Dyn. Sist. A (2018), preprint at: arxiv.
8. Characterizations of monotonicity of vector fields on metric measure space, Cal.Var.PDE. (2018), preprint at: arxiv.
9. Sharp p-Poincaré inequality under Measure Contraction Property, Manuscripta Math. (2020) , preprint at : arxiv.
10. Measure rigidity of synthetic lower Ricci curvature bound on Riemannian manifolds, Adv. Math. (2020), preprint at: arxiv.
11. (with E. Milman) Sharp Poincaré inequality under Measure Contraction Property, Ann. Scuola Norm. Sup. Pisa Cl. Sci. (2021), preprint at: arxiv.
12. Rigidity of some functional inequalities on RCD spaces, J.Math.Pures Appl. (2021) preprint at: arxiv.
13. (with K-T. Sturm) Curvature-dimension conditions for diffusions under time change, Ann. Math. Pura Appl . (2022), preprint at: arxiv.
14. (with A. Pinamonti) On the asymptotic behaviour of the fractional Sobolev seminorms in metric measure spaces: Bourgain-Brezis-Mironescu's theorem revisited, preprint at: arxiv.
15. (with A. Pinamonti) On the asymptotic behaviour of the fractional Sobolev seminorms in metric measure spaces: asymptotic volume ratio, volume entropy and rigidity, preprint at: arxiv.
16. Sharp and rigid isoperimetric inequality in metric measure spaces with non-negative Ricci curvature, , preprint at: arxiv.
Preprints not for publication:
A sharp isoperimetric inequality in metric measure spaces with non-negative Ricci curvature, preprint at: arxiv.
Ricci tensor on smooth metric measure space with boundary, preprint at: arxiv.