arXiv subjects

Zhexing Zhang

Publications and source records attributed to Zhexing Zhang.

3 recordsLinked to original sources

arXiv2026

Strichartz and Spectral Projection Estimates on Asymptotically Conic Manifolds

We prove the lossless unit interval Strichartz theorem on asymptotically conic surfaces, assuming that a large enough neighborhood of its trapped set has negative curvature. We also prove the spectral projection theorem on surfaces with Euclidean ends and nonpositive curvature, assuming a large enough neighborhood of its trapped set has negative curvature. We also discuss the spectral projection theorem on asymptotically Euclidean manifolds with dimension greater than or equal to 3, assuming some local smoothing estimates.

math.DG↗

arXiv2025

Spectral projection estimates restricted to uniformly embedded submanifolds

Let $M$ be a manifold with nonpositive sectional curvature and bounded geometry, and let $\Sigma$ be a uniformly embedded submanifold of $M.$ We estimate the $L^2(M)\to L^q(\Sigma)$ norm of a $\log$-scale spectral projection operator. It is a generalization of result of X. Chen to noncompact cases. We also prove sharp spectral projection estimates of spectral windows of any small size restricted to nontrapped geodesics on even asymptotically hyperbolic surfaces with bounded geometry and curvature pinched below 0.

math.DG↗

arXiv2025

Lossless Strichartz and spectral projection estimates on unbounded manifolds

We prove new lossless Strichartz and spectral projection estimates on asymptotically hyperbolic surfaces, and, in particular, on all convex cocompact hyperbolic surfaces. In order to do this, we also obtain log-scale lossless Strichartz and spectral projection estimates on manifolds of uniformly bounded geometry with nonpositive and negative sectional curvatures, extending the recent works of the first two authors for compact manifolds. We are able to use these along with known $L^2$-local smoothing and new $L^2 \to L^q$ half-localized resolvent estimates to obtain our lossless bounds.

math.AP↗