Existence and Scattering for Solutions to Semilinear Wave Equations on High Dimensional Hyperbolic Space

TL;DR

This paper establishes global existence and scattering results for small solutions to semilinear wave equations with high-power nonlinearities on high-dimensional hyperbolic spaces, extending understanding of wave behavior in curved geometries.

Contribution

It proves small-data global existence and asymptotic completeness for semilinear wave equations with high-power nonlinearities on hyperbolic spaces of dimension three or higher.

Findings

Global existence for small initial data.

Existence and asymptotic completeness of wave operators.

Results apply to nonlinearities with sufficiently high integer powers.

Abstract

We prove small-data global existence to semi-linear wave equations on hyperbolic space of dimension greater than or equal to three, for nonlinearities that have the form of a sufficiently high integer power of the solution. We also prove the existence and asymptotic completeness of wave operators in this setting.