负曲率统计流形上的信息几何与混沌

Lower bounds for Cauchy data on curves in a negatively curved surface

We prove a uniform lower bound on Cauchy data on an arbitrary curve on a negatively curved surface using the Dyatlov-Jin(-Nonnenmacher) observability estimate on the global surface. In the process, we prove some further results about defect measures of restrictions of eigenfunctions to a hypersurface.

Boundary rigidity of negatively-curved asymptotically hyperbolic surfaces

In the spirit of Otal and Croke, we prove that a negatively-curved asymptotically hyperbolic surface is boundary distance rigid, where the distance between two points on the boundary at infinity is defined by a renormalized quantity.

On the existence and stability of blowup for wave maps into a negatively curved target

We consider wave maps on $(1+d)$-dimensional Minkowski space. For each dimension $d\geq 8$ we construct a negatively curved, $d$-dimensional target manifold that allows for the existence of a self-similar wave map which provides a stable blowup mechanism for the corresponding Cauchy problem.

李群上的负曲左不变度量

Negatively curved left-invariant metrics on Lie groups

我们讨论了负弯曲的齐性空间，它允许一个单传递的等距群，或者等价地，李群上的负弯曲的左不变度量。负弯曲的空间具有非常丰富和多样的结构，从数学和物理的角度来看都很有趣。除了给出具有负Ricci曲率标量的左不变度量的一般准则外，我们还考虑了特殊情况，如爱因斯坦空间和Ricci零孤子。我们指出了这些空间在一些高维引力理论中的相关性。特别是，我们表明，里奇nilsolitons黎曼解决方案，某些高曲率引力理论。

负曲率黎曼流形上斯托克斯方程解的非唯一性

Nonuniqueness of solutions of the Navier-Stokes equations on negatively curved Riemannian manifolds

在一个著名的工作，M。Anderson构造了一个Hadamard流形$(M^n, g)$，当$p \neq n/2$时，它带有非零的$L^2$调和$p$ -形式，从而反驳了Dodziuk-Singer猜想.本文利用流形$(M^3, g)$解决了几何分析中的另一个问题，即Navier-斯托克斯方程的Leray-Hopf型解的非唯一性.

负曲面上半经典薛定谔方程的扰动

Perturbation of the semiclassical Schrödinger equation on negatively curved surfaces

研究了紧致负曲面上的半经典薛定谔方程。对于任何序列的初始数据microlocalized上的单位余切丛，我们看看量子演化（以下的Eschlafest时间）小扰动下的薛定谔方程，我们证明，在半经典极限和典型的扰动，解决方案成为均匀分布的单位余切丛。