类时洛伦兹程函方程的柯西型问题的粘性解

全局双曲时空上 Lorentzian eikonal 方程的全局粘性解

Global viscosity solutions to Lorentzian eikonal equation on globally hyperbolic space-times

本文研究全局双曲时空上的 Lorentzian eikonal 方程，证明类距离全局粘性解的存在性，并按时间方向一致性分析其局部变分表示、半凹性及非一致情形的特殊性质。

洛伦兹Calderón问题的反例

Counterexamples to the Lorentzian Calderón problem

研究显示非等距的光滑全球超曲面洛伦兹度量在无限圆柱体上具有相同的超几何狄利克雷到神经元映射

从单点非线性波观测确定洛伦兹流形

Determining Lorentzian manifold from non-linear wave observation at a single point

本文研究非线性双曲方程的反问题，证明通过单条类时曲线上的源到解映射可确定洛伦兹流形的共形结构，方法为非线性波相互作用的微局部分析。

通过最优运输研究时状里奇曲率下界：Orlicz型洛伦兹成本函数

Timelike Ricci curvature lower bounds via optimal transport for Orlicz-type Lorentzian costs

本文研究了全局超曲时空上的最优运输问题，针对Orlicz型洛伦兹成本函数u∘ℓ，提出u-分离概念并获得强对偶性，通过几何熵凸性刻画时状里奇曲率下界。

Fundamental solutions for the wave operator on static Lorentzian manifolds with timelike boundary

We consider the wave operator on static, Lorentzian manifolds with timelike boundary and we discuss the existence of advanced and retarded fundamental solutions in terms of boundary conditions. By means of spectral calculus we prove that answering this question is equivalent to studying the self-adjoint extensions of an associated elliptic operator on a Riemannian manifold with boundary $(M,g)$. The latter is diffeomorphic to any, constant time hypersurface of the underlying background. In turn, assuming that $(M,g)$ is of bounded geometry, this problem can be tackled within the framework of b…

The Dirichlet-to-Neumann map for a semilinear wave equation on Lorentzian manifolds

We consider the semilinear wave equation $\Box_g u+a u^4=0$, $a\neq 0$, on a Lorentzian manifold $(M,g)$ with timelike boundary. We show that from the knowledge of the Dirichlet-to-Neumann map one can recover the metric $g$ and the coefficient $a$ up to natural obstructions. Our proof rests on the analysis of the interaction of distorted plane waves together with a scattering control argument, as well as Gaussian beam solutions.