6 papers
A Unified Quermassintegral Approach to Quasilinear Heat Dispersion and Loss
Xiaoshang Jin, Jie Xiao
This paper establishes a fundamental connection between quasilinear potential theory and convex geometric analysis by investigating the interplay between the quasilinear Laplace op…
Sharp -Capacity Estimates via Quermassintegrals in Hyperbolic Space
Xiaoshang Jin, Yao Wan, Jie Xiao
This paper establishes sharp upper bounds for -capacities in the hyperbolic space through hyperbolic quermassintegrals and effective c…
Capacities-to-masses for Laplace-Beltrami operators on complete Riemannian manifolds
Xiaoshang Jin, Jie Xiao
This paper presents an innovative approach to the capacities-to-masses for the Laplace-Beltrami operators on the complete Riemannian manifolds, unexpectedly solving the open proble…
Heat dispersion laws in smooth compact manifolds
Xiaoshang Jin, Jie Xiao
Given a Lipschitz conductor in the smooth compact Riemannian -manifold , such a half generic heat dispersion law $$ {\rm H^d}_{p,\varPhi,\varPsi}(K,M)=2^{-1} {\r…
Essential -capacity-volume estimates for rotationally symmetric manifolds
Xiaoshang Jin, Jie Xiao
Given , this article presents the novel basic volumetric estimates for the relative -capacities with their applications to finding not only the sharp weak $(p,q…
Sharply estimating hyperbolic capacities
Xiaoshang Jin, Jie Xiao
This paper is devoted to establishing four types of sharp capacitary inequalities within the hyperbolic space as detailed in Theorems 2.1-3.1-4.1-5.1.