Decay for the wave and Schroedinger evolutions on manifolds with conical ends, Part II

TL;DR

This paper establishes global dispersive estimates for Schrödinger and wave equations on manifolds with conical ends, focusing on initial data with fixed nonzero angular momentum, despite the presence of trapping in the Hamiltonian flow.

Contribution

It extends dispersive estimate results to manifolds with conical ends considering trapped Hamiltonian flow and fixed nonzero angular momentum.

Findings

Proves global dispersive estimates for Schrödinger and wave evolutions.

Handles cases with trapping in Hamiltonian flow.

Focuses on initial data with fixed nonzero angular momentum.

Abstract

Global in time dispersive estimates for the Schroedinger and wave evolutions are obtained on manifolds with conical ends whose Hamiltonian flow exhibits trapping. This paper deals with the case of initial data with fixed "nonzero angular momentum".