Strichartz estimates for convex co-compact hyperbolic surfaces

TL;DR

This paper proves that Strichartz estimates for the Schrödinger equation are valid on convex co-compact hyperbolic surfaces with only a minimal loss of regularity, leveraging recent advances by Bourgain-Dyatlov.

Contribution

It establishes Strichartz estimates with arbitrarily small regularity loss on a broad class of hyperbolic surfaces, extending previous results.

Findings

Strichartz estimates hold with small loss of regularity

Applicable to all convex co-compact hyperbolic surfaces

Builds on recent Bourgain-Dyatlov work

Abstract

Using recent work of Bourgain-Dyatlov we show that for any convex co-compact hyperbolic surface Strichartz estimates for the Schr\"odinger equation hold with an arbitrarily small loss of regularity.