2 citations · 8 across the 14 of their papers we have counts for
16 papers
Bouncing-ball modes in ergodic billiards
Zhenhao Li, Maciej Zworski
We show that for a horizontally stretched Bunimovich billiard, for almost every stretching parameter, there exists a sequence of eigenfunctions concentrating in the rectangular par…
Continuity equation on metric spaces via measure-valued derivations and BV-Wasserstein curves
Ehsan Abedi, Zhenhao Li, Timo Schultz
We introduce a notion of continuity equation on metric spaces that is capable of describing curves of probability measures which are absolutely continuous, and more generally of bo…
Synthetic approaches to Ricci flows
Matthias Erbar, Marco Flaim, Eric Hupp +3
We review different notions of synthetic Ricci flow that apply to time-dependent families of metric measure spaces and which are based on properties of the heat flow, ideas from op…
Evolution of internal waves in a 2D subcritical channel
Zhenhao Li, Jian Wang, Jared Wunsch
We study the long time evolution of internal waves in two dimensional subcritical channels with flat horizontal ends. We show the leading profiles of solutions are the outgoing sol…
On the rigidity of Wasserstein contraction along heat flows
Zhenhao Li
We establish an equivalence between the rigidity of Wasserstein contraction along heat flows and the rigidity of Bakry--Émery gradient estimates for Lipschitz functions. Applying r…
Synthetic notions of Ricci flow for metric measure spaces
Matthias Erbar, Zhenhao Li, Timo Schultz
We develop different synthetic notions of Ricci flow in the setting of time-dependent metric measure spaces based on ideas from optimal transport. They are formulated in terms of d…
Internal waves in a 2D subcritical channel
Zhenhao Li, Jian Wang, Jared Wunsch
We analyze the scattering of linear internal waves in a two dimensional channel with subcritical bottom topography. We construct the scattering matrix for the internal wave problem…
Long time quantum-classical correspondence for open systems in trace norm
Zhenhao Li
We consider a frictionless system coupled to an external Markovian environment. The quantum and classical evolution of such systems are described by the Lindblad and the Fokker-Pla…
Internal waves in aquariums with characteristic corners
Zhenhao Li
We give a precise microlocal description of the singular profile that forms in the long-time propagation of internal waves in an effectively two-dimensional aquarium. We allow doma…
Internal waves in 2D domains with ergodic classical dynamics
Yves Colin de Verdière, Zhenhao Li
We study a model of internal waves in an effectively 2D aquarium under periodic forcing. In the case when the underlying classical dynamics has sufficiently irrational rotation num…
2D internal waves in an ergodic setting
Zhenhao Li
We study a model of internal waves under periodic forcing in an effectively 2-dimensional aquarium. When the underlying classical dynamics has sufficiently irrational rotation numb…
The Globalization Theorem for CD(K,N) on locally finite Spaces
Zhenhao Li
We establish the local-to-global property of the synthetic curvature-dimension condition for essentially non-branching locally finite metric-measure spaces, extending the work [F.…
On the Smoothness and Regularity of the Chess Billiard Flow and the Poincaré Problem
Sally Zhu, Zhenhao Li
The Poincaré problem is a model of two-dimensional internal waves in stable-stratified fluid. The chess billiard flow, a variation of a typical billiard flow, drives the formation…
Absolutely continuous and BV-curves in 1-Wasserstein spaces
Ehsan Abedi, Zhenhao Li, Timo Schultz
We extend the result of Lisini (Calc Var Partial Differ Equ 28:85-120, 2007) on the superposition principle for absolutely continuous curves in -Wasserstein spaces to the specia…
Weyl Laws for Open Quantum Maps
Zhenhao Li
We find Weyl upper bounds for the quantum open baker's map in the semiclassical limit. For the number of eigenvalues in an annulus, we derive the asymptotic upper bound $\mathcal O…
Uniqueness of excited states to in three dimensions
Alex Cohen, Zhenhao Li, Wilhelm Schlag
We prove the uniqueness of several excited states to the ODE , , and for the model nonlinearity $f(y) =…