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Renormalized Volume and Area

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posted on 2021-07-08, 00:00 authored by Aaron Tyrrell

In this dissertation we look at some problems on renormalized volume and area. We develop a Chern-Gauss-Bonnet formula for the renormalized area of a hypersurface within a 5-dimensional Poincaré-Einstein manifold. This is followed by an investigation into renormalized area in the Singular Yamabe setting. Lastly, we look at the renormalized volume of a minimally bounded region within a 4-dimensional Poincaré-Einstein manifold.

History

Date Modified

2021-09-08

Defense Date

2021-04-30

CIP Code

  • 27.0101

Research Director(s)

Matthew J. Gursky

Committee Members

Nick Edelen Qing Han Gerard Misiolek

Degree

  • Doctor of Philosophy

Degree Level

  • Doctoral Dissertation

Alternate Identifier

1262585638

Library Record

6102798

OCLC Number

1262585638

Program Name

  • Mathematics

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