Decay estimates for the Schroedinger evolution on asymptotically conic surfaces of revolution I

TL;DR

This paper proves a decay estimate for the Schrödinger equation on a specific non-compact surface of revolution with a trapped geodesic, demonstrating dispersive behavior over time.

Contribution

It establishes a uniform dispersive estimate for Schrödinger evolution on asymptotically conic surfaces with trapping, extending previous results to more complex geometries.

Findings

Proves a 1/t decay estimate valid for all times.

Demonstrates dispersive behavior on surfaces with trapped geodesics.

Extends decay estimates to asymptotically conic geometries.

Abstract

We establish a dispersive estimate (with a decay of 1/t), valid for all times, for the Schroedinger evolution on a non-compact 2-dimensional manifold with a trapped geodesic.