17 citations · 154 across the 69 of their papers we have counts for
70 papers
Capacitary Trapping and Brownian Escape: A Sharp Hardy Principle for Absorbing Media
Yiqun Chen, Jie Xiao, Dachun Yang +2
We study Brownian motion killed upon exiting arbitrary open sets , . Let . The infimal radius at which the abs…
A Minkowski Theory for the Exterior Capacitary Volumes and A Resolution of the Pólya-Szegö Conjecture
Qiushuang Liu, Jie Xiao, Ning Zhang +2
This paper establishes a unified Minkowski theory for exterior p-capacitary volumes and resolves the classical Pólya-Szegö conjecture on the electrostatic capacity of convex bodies…
The iterated geometric Green's formula
Chao Shen, Jie Xiao
Fang, Lan, and Xiao established the geometric Green's formula as a categorical isomorphism for arbitrary semisimple complexes. In this short note, we generalize their work to multi…
Sheaf realization of Bridgeland's Hall algebra of Dynkin type
Jiepeng Fang, Yixin Lan, Jie Xiao
As one of results in [6], Bridgeland realized the quantum group via the localization of Ringel-Hall algebra for the two-periodic projective complexes of quiver repre…
The correspondence between the canonical and semicanonical bases
Jiepeng Fang, Yixin Lan, Jie Xiao
Given any symmetric Cartan datum, Lusztig has provided a pair of key lemmas to construct the perverse sheaves over the corresponding quiver and the functions of irreducible compone…
The Multiplication Formulas of Weighted Quantum Cluster Functions
Zhimin Chen, Jie Xiao, Fan Xu
By applying the property of Ext-symmetry and the affine space structure of certain fibers, we introduce the notion of weighted quantum cluster functions and prove their multiplicat…