3 papers
math.MG2026
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 bodi…
math.RT2026
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…
math.RT2025
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…