52 citations · 168 across the 14 of their papers we have counts for
14 papers
Counting Pollicott--Ruelle resonances for Axiom A flows
Long Jin, Zhongkai Tao
In this paper, we count the number of Pollicott--Ruelle resonances for open hyperbolic systems and Axiom A flows. In particular, we prove polynomial upper bounds and sublinear lowe…
Flat trace estimates for Anosov flows
Long Jin, Zhongkai Tao
We prove a high energy flat trace estimate for the modified resolvent of the generator of an Anosov flow. This fills a gap in the proof of the local trace formula in [Jin-Zworski '…
Control of eigenfunctions on surfaces of variable curvature
Semyon Dyatlov, Long Jin, Stéphane Nonnenmacher
We prove a microlocal lower bound on the mass of high energy eigenfunctions of the Laplacian on compact surfaces of negative curvature, and more generally on surfaces with Anosov g…
Damped wave equations on compact hyperbolic surfaces
Long Jin
We prove exponential decay of energy for solutions of the damped wave equation on compact hyperbolic surfaces with regular initial data as long as the damping is nontrivial. The pr…
Fractal Uncertainty Principle with Explicit Exponent
Long Jin, Ruixiang Zhang
We prove an explicit formula for the dependence of the exponent in the fractal uncertainty principle of Bourgain-Dyatlov on the dimension and on the regularity constant for the reg…
Control for Schrödinger equation on hyperbolic surfaces
Long Jin
We show that the any nonempty open set on a hyperbolic surface provides observability and control for the time dependent Schrödinger equation. The only other manifolds for which th…