Cut and conjugate points of the exponential map, with applications
Analysis of PDEs
2014-11-17 v1 Differential Geometry
Abstract
The goal of this thesis is to study the singularities of the exponential map of Riemannian and Finsler manifolds (a concept related to caustics and catastrophes), and the object known as the cut locus (aka ridge, medial axis or skeleton), to improve existing results about its structure, to look at it in new ways, and to derive applications to the Ambrose conjecture and the Hamilton-Jacobi equations.
Keywords
Cite
@article{arxiv.1411.3933,
title = {Cut and conjugate points of the exponential map, with applications},
author = {Pablo Angulo Ardoy},
journal= {arXiv preprint arXiv:1411.3933},
year = {2014}
}
Comments
Doctoral thesis, U. Madrid, 122 pages, 23 figures, official version with some errata corrected, defended on October 17, 2014, figures a bit out of place on this arxiv version, but it's fine otherwise