5 citations · 18 across the 9 of their papers we have counts for
9 papers
Initial data gluing in the asymptotically flat regime via solution operators with prescribed support properties
Yuchen Mao, Sung-Jin Oh, Zhongkai Tao
We give new proofs of general relativistic initial data gluing results on unit-scale annuli based on explicit solution operators for the linearized constraint equation around the f…
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…
The fractal uncertainty principle via Dolgopyat's method in higher dimensions
Aidan Backus, James Leng, Zhongkai Tao
We prove a fractal uncertainty principle with exponent , , for Ahlfors--David regular subsets of with dimension whi…
Spectral asymptotics for kinetic Brownian motion on Riemannian manifolds
Qiuyu Ren, Zhongkai Tao
We prove the convergence of the spectrum of the generator of the kinetic Brownian motion to the spectrum of the base Laplacian for closed Riemannian manifolds. This generalizes rec…
Localized initial data for Einstein equations
Yuchen Mao, Zhongkai Tao
We apply a new method with explicit solution operators to construct asymptotically flat initial data sets of the vacuum Einstein equation with new localization properties. Applicat…
Spectral asymptotics for kinetic Brownian motion on locally symmetric spaces
Qiuyu Ren, Zhongkai Tao
We prove the strong convergence of the spectrum of the kinetic Brownian motion to the spectrum of base Laplacian for a large class of compact locally Riemannian homogeneous spaces,…
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 '…
Exact Control for Schrödinger Equation on Torus
Zhongkai Tao
For standard torus , we prove observability for free Schrödinger equation from a ball of radius with explicit dependence of the observab…
0-th Order Pseudo-differential Operator on the Circle
Zhongkai Tao
In this paper we consider 0-th order pseudodifferential operators on the circle. We show that inside any interval disjoint from critical values of the principal symbol, the spectru…