C. Sogge

activity

20242026

collaborators

7 papers

math.AP2026

Lossless Strichartz and spectral projection estimates on unbounded manifolds

Xiaoqi Huang, Christopher D. Sogge, Zhongkai Tao +1

We prove new lossless Strichartz and spectral projection estimates on asymptotically hyperbolic surfaces, and, in particular, on all convex cocompact hyperbolic surfaces. In order…

math.AP2025

Strichartz estimates for the SchrÃ¶dinger equation on Zoll manifolds

Xiaoqi Huang, Christopher D. Sogge

We obtain optimal space-time estimates in $L_{t, x}^{q}$ spaces for all $q \geq 2$ for solutions to the SchrÃ¶dinger equation on Zoll manifolds, including, in particular, the standard r…

math.AP2025

Curvature and sharp growth rates of log-quasimodes on compact manifolds

Xiaoqi Huang, Christopher D. Sogge

We obtain new optimal estimates for the $L^{2} (M) \to L^{q} (M)$ , $q \in (2, q_{c}]$ , $q_{c} = 2 (n + 1) / (n - 1)$ , operator norms of spectral projection operators associated with spectral windows $[Î…

math.AP2024

Strichartz estimates for the SchrÃ¶dinger equation on compact manifolds with nonpositive sectional curvature

Xiaoqi Huang, Christopher D. Sogge

We obtain improved Strichartz estimates for solutions of the SchrÃ¶dinger equation on compact manifolds with nonpositive sectional curvatures which are related to the classical uni…

math.AP2024

Curvature and harmonic analysis on compact manifolds

Christopher D. Sogge

We discuss problems that relate curvature and concentration properties of eigenfunctions and quasimodes on compact boundaryless Riemannian manifolds. These include new sharp $L^{q}$ -…

math.AP2024

Quasimode concentration on compact space forms

Xiaoqi Huang, Christopher D. Sogge

We show that the upper bounds for the $L^{2}$ -norms of $L^{1}$ -normalized quasimodes that we obtained in [9] are always sharp on any compact space form. This allows us to characterize…