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…
Semiclassical measures on hyperbolic surfaces have full support
Semyon Dyatlov, Long Jin
We show that each limiting semiclassical measure obtained from a sequence of eigenfunctions of the Laplacian on a compact hyperbolic surface is supported on the entire cosphere bun…
Exponential lower resolvent bounds far away from trapped sets
Kiril Datchev, Long Jin
We give examples of semiclassical Schrödinger operators with exponentially large cutoff resolvent norms, even when the supports of the cutoff and potential are very far apart. The…
Dolgopyat's method and the fractal uncertainty principle
Semyon Dyatlov, Long Jin
We show a fractal uncertainty principle with exponent , , for Ahflors-David regular subsets of of dimension . This improves over the volume bo…
Resonances for open quantum maps and a fractal uncertainty principle
Semyon Dyatlov, Long Jin
We study eigenvalues of quantum open baker's maps with trapped sets given by linear arithmetic Cantor sets of dimensions . We show that the size of the spectral gap is…
A local trace formula for Anosov flows (with an appendix by Frédéric Naud)
Long Jin, Frédéric Naud, Maciej Zworski
We prove a local trace formula for Anosov flows. It relates Pollicott--Ruelle resonances to the periods of closed orbits. As an application, we show that the counting function for…
Scattering Resonances of Convex Obstacles for general boundary conditions
Long Jin
We study the distribution of resonances for smooth strictly convex obstacles under general boundary conditions. We show that under a pinched curvature condition for the boundary of…
Semiclassical Cauchy Estimates and Applications
Long Jin
In this note, we study solutions to semiclassical Schrodinger equations on a real analytic manifold with a real analytic potential and prove the semiclassical version of Cauchy est…
Resonance-free Region in scattering by a strictly convex obstacle
Long Jin
We prove the existence of a resonance free region in scattering by a strictly convex obstacle with the Robin boundary condition. More precisely, we show that the scattering resonan…