Wave equations on asymptotically de Sitter spaces

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Abstract/Contents

Abstract: Asymptotically de Sitter spaces are Lorentzian manifolds modeled on the de Sitter space of general relativity. In this dissertation, we construct the forward fundamental solution for the wave and Klein-Gordon equations on asymptotically de Sitter spaces. We adapt classes of conormal and paired Lagrangian distributions to this setting and show that the lift of the kernel of the forward fundamental solution to a blown-up space is a sum of distributions in these classes. We use the structure of the kernel of the fundamental solution to study its mapping properties. We show that Strichartz estimates with loss hold for the positive mass Klein-Gordon equation on asymptotically de Sitter spaces. When the mass parameter is the conformal value, Strichartz estimates hold without loss. As an application of these estimates, we prove a small-data global existence result for a defocusing Klein-Gordon equation.

Type of resource	text
Form	electronic; electronic resource; remote
Extent	1 online resource.
Publication date	2010
Issuance	monographic
Language	English

Associated with	Baskin, Dean Russell
Associated with	Stanford University, Department of Mathematics
Primary advisor	Mazzeo, Rafe
Thesis advisor	Mazzeo, Rafe
Thesis advisor	Brendle, Simon, 1981-
Thesis advisor	Schoen, Richard (Richard M.)
Thesis advisor	Vasy, András
Advisor	Brendle, Simon, 1981-
Advisor	Schoen, Richard (Richard M.)
Advisor	Vasy, András

Genre	Theses

Statement of responsibility	Dean Russell Baskin.
Note	Submitted to the Department of Mathematics.
Thesis	Ph.D. Stanford University 2010
Location	electronic resource

License: This work is licensed under a Creative Commons Attribution Non Commercial 3.0 Unported license (CC BY-NC).

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