12 citations · 40 across the 12 of their papers we have counts for
12 papers
Partial Plateau's Problem with -mass
Enrique Alvarado, Qinglan Xia
Classically, Plateau's problem asks to find a surface of the least area with a given boundary . In this article, we investigate a version of Plateau's problem, where the boundar…
On the Curvature of Metric Triples
Qinglan Xia
In this article, we introduce a notion of curvature, denoted by , for a metric triple inside a (possibly discrete) metric space . Such a notion enables us to consid…
Ramified optimal transportation with payoff on the boundary
Qinglan Xia, Shaofeng Xu
This paper studies a variant of ramified/branched optimal transportation problems. Given the distributions of production capacities and market sizes, a firm looks for an allocation…
The existence of minimizers for an isoperimetric problem with Wasserstein penalty term in unbounded domains
Qinglan Xia, Bohan Zhou
In this article, we consider the (double) minimization problem $$\min\left\{P(E;Ω)+λW_p(E,F):~E\subseteqΩ,~F\subseteq \mathbb{R}^d,~\lvert E\cap F\rvert=0,~ \lvert E\rvert=\lvert F…
A fractal shape optimization problem in branched transport
Paul Pegon, Filippo Santambrogio, Qinglan Xia
We investigate the following question: what is the set of unit volume which can be best irrigated starting from a single source at the origin, in the sense of branched transport? W…
General fractals represented by -limit sets of compression maps
Tynan Lazarus, Enrique G Alvarado, Qinglan Xia
In this article, we provide a simple and systematic way to represent general (inhomogeneous) fractals that may look different at different scales and places. By using set-valued co…
On the Ramified Optimal Allocation Problem
Qinglan Xia, Shaofeng Xu
This paper proposes an optimal allocation problem with ramified transport technology in a spatial economy. Ramified transportation is used to model the transport economy of scale i…
The Exchange Value Embedded In A Transport System
Qinglan Xia, Shaofeng Xu
This paper shows that a well designed transport system has an embedded exchange value by serving as a market for potential exchange between consumers. Under suitable conditions, on…
Ramified optimal transportation in geodesic metric spaces
Qinglan Xia
An optimal transport path may be viewed as a geodesic in the space of probability measures under a suitable family of metrics. This geodesic may exhibit a tree-shaped branching str…
On the transport dimension of measures
Qinglan Xia, Anna Vershynina
In this article, we define the transport dimension of probability measures on using ramified optimal transportation theory. We show that the transport dimension of a…
Numerical simulation of optimal transport paths
Qinglan Xia
This article provides numerical simulation of an optimal transport path from a single source to an atomic measure of equal total mass. We first construct an initial transport path,…
The geodesic problem in quasimetric spaces
Qinglan Xia
In this article, we study the geodesic problem in a generalized metric space, in which the distance function satisfies a relaxed triangle inequality f…