14 papers
Nonradial stable solutions near the Joseph--Lundgren threshold
Shibing Chen, Yong Liu, Juncheng Wei +1
We study positive stable solutions of the supercritical Lane--Emden equation in the first Joseph--Lundgren interval. For a family of dimensions, we construct nonradial stable entir…
Global Regularity in Optimal Transport
Shibing Chen, Yuanyuan Li, Xianduo Wang
In this paper we establish global estimates for the convex potentials of quadratic optimal transport between bounded convex domains with continuous positive densities. Al…
The many-body Blaschke-Santaló type inequality via optimal transport
Shibing Chen, Yuanyuan Li, Dongmeng Xi +1
Let be origin-symmetric measurable sets of finite volume such that \[ \sum_{1\le i<j\le k}\langle x_i,x_j\rangle\le \binom{k}{2}, \qquad \forall\…
The Mahler Conjecture in Three Dimensions
Shibing Chen, Yuanyuan Li, Dongmeng Xi +1
The Mahler conjecture dates back to 1938. This paper solves the conjecture for general convex bodies in three dimensions by developing a method called the shadow flow. The equality…
Symmetry breaking for the complex sine-Gordon equation
Shibing Chen, Changfeng Gui, Yong Liu +2
We consider the existence of vortex solutions to the complex sine-Gordon II (CSG2) equation, which can be viewed as an analogy of the Ginzburg-Landau (GL) equation. Using the nontr…
Optimal (partial) transport to non-convex polygonal domains
Shibing Chen, Yuanyuan Li, Jiakun Liu
In this paper, we investigate optimal (partial) transport problems for which the target is a non-convex polygonal domain in \(\mathbb{R}^2\). For the complete optimal transport pro…