17 citations · 154 across the 69 of their papers we have counts for
8 papers · 1 filter
p-capacity vs surface-area
Jie Xiao
This paper is devoted to exploring the relationship between the -capacity and the surface-area in which especially shows: if …
Optimal geometric estimates for fractional Sobolev capacities
Jie Xiao
This note develops certain sharp inequalities relating the fractional Sobolev capacity of a set to its standard volume and fractional perimeter.
Towards Conformal Capacities in Euclidean Spaces
Jie Xiao
This paper addresses the so-called conformal capacities in , , through comparing three existing definitions (due to Betsakos, Colesanti-Cuoghi, Anderson-Vamana…
A Maximum Problem of S.-T. Yau for Variational p-Capacity
Jie Xiao
Through using the semidiameter (in connection to: the mean radius and surface radius) of a convex closed hypersurface in as an sharp upper bound of the variati…
The Semi-linear Torsional Rigidity on a Complete Riemannian Two-Manifold
Jie Xiao
This note is concerned with some essential properties (optimal isoperimetry, first variation, and monotonicity formula) of the so-called -torsional rigidity $\mathcal{T}…
Toward Best Isoperimetric Constants for -Normal Conformal Metrics on ,
Jie Xiao
The aim of this article is: (a) To establish the existence of the best isoperimetric constants for the -normal conformal metrics on , $n\ge 3…