Nonlinear waves on 3D hyperbolic space

Metcalfe, Jason; Taylor, Michael

doi:10.1090/S0002-9947-2011-05122-6

Nonlinear waves on 3D hyperbolic space
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Trans. Amer. Math. Soc. 363 (2011), 3489-3529 Request permission

Abstract:

In this article, global-in-time dispersive estimates and Strichartz estimates are explored for the wave equation on three dimensional hyperbolic space. Due to the negative curvature, extra dispersion is noted, as compared to the Euclidean case, and a wider range of Strichartz estimates is proved. Using these, small data global existence to semilinear wave equations is shown for a range of powers that is broader than that known for Euclidean space.

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