4 papers
On Aubry's completeness conjecture
Tianqi Shi, Jinxin Xue
In this paper, we prove Aubry's completeness stating conjecture that for a twist map the graph of rotation numbers as a function of the cohomology classes is a purely singularly co…
Singularities and their propagation in optimal transport
Piermarco Cannarsa, Wei Cheng, Tianqi Shi +1
In this paper, we investigate the singularities of potential energy functionals \(ϕ(\cdot)\) associated with semiconcave functions \(ϕ\) in the Borel probability measure space and…
Optimal transport in the frame of abstract Lax-Oleinik operator revisited
Wei Cheng, Jiahui Hong, Tianqi Shi
This is our first paper on the extension of our recent work on the Lax-Oleinik commutators and its applications to the intrinsic approach of propagation of singularities of the vis…
Viscosity solutions to a Cauchy type problem for timelike Lorentzian eikonal equation
Siyao Zhu, Xiaojun Cui, Tianqi Shi
In this paper, we propose a Cauchy type problem to the timelike Lorentzian eikonal equation on a globally hyperbolic space-time. For this equation, as the value of the solution on…