Mathematical Physics


A Treatise on Information Geometry

Authors: Christopher Goddard

In early 1999, Professor Frieden of the University of Arizona published a book through Cambridge University Press titled "Physics from Fisher Information". It is the purpose of this dissertation to further develop some of his ideas, as well as explore various exotic differentiable structures and their relationship to physics. In addition to the original component of this work, a series of survey chapters are provided, in the interest of keeping the treatise self-contained. The first summarises the main preliminary results on the existence of non-standard structures on manifolds from the Milnor-Steenrod school. The second is a standard introduction to semi-riemannian geometry. The third introduces the language of geometric measure theory, which is important in justifying the existence of smooth solutions to variational problems with smooth structures and smooth integrands. The fourth is a short remark on PDE existence theory, which is needed for the fifth, which is essentially a typeset version of a series of lectures given by Ben Andrews and Gerhard Huisken on the Hamilton-Perelman program for proving the Geometrisation Conjecture of Bill Thurston.

Comments: 301 Pages. From the ResearchGate listing, per the article:

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Submission history

[v1] 19 Aug 2009 (removed)
[v2] 1 Nov 2009 (removed)
[v3] 15 Jan 2010 (removed)
[v4] 2017-07-05 17:02:25

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