Alavipour, Mehrad (2022) Relation Between Geodesic Polar and Isothermal Coordinates. Masters thesis, Concordia University.
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Abstract
The main result of this thesis is an asymptotic formula establishing a correspondence between two at first sight unrelated systems of local coordinates on a two-dimensional real analytic Riemannian manifold: the so-called isothermal local parameter and the Riemann normal coordinates. This formula was stated without proof in 1992 Fay’s memoir on analytic torsion, a weaker statement was proved in Walsh’s 2012 PhD thesis. A survey of basic facts from differential geometry used in our proof is also given.
| Divisions: | Concordia University > Faculty of Arts and Science > Mathematics and Statistics |
|---|---|
| Item Type: | Thesis (Masters) |
| Authors: | Alavipour, Mehrad |
| Institution: | Concordia University |
| Degree Name: | M. Sc. |
| Program: | Mathematics |
| Date: | May 2022 |
| Thesis Supervisor(s): | Kokotov, Alexey and Korotkin, Dmitry |
| ID Code: | 990574 |
| Deposited By: | Mehrad Alavipour |
| Deposited On: | 27 Oct 2022 14:34 |
| Last Modified: | 27 Oct 2022 14:34 |
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