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Cut and conjugate points of the exponential map, with applications

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arxiv 1411.3933 v1 pith:3MVKEPPT submitted 2014-11-14 math.AP math.DG

Pablo Angulo Ardoy This is my paper · ORCID
classification math.APmath.DG
keywords applicationsexponentialambroseaxiscatastrophescausticsconceptconjecture
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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.

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  1. Total curvature and the isoperimetric inequality in Cartan-Hadamard manifolds

    math.DG 2019-08 accept novelty 7.0 of 10

    The paper proves in all dimensions that the total curvature inequality implies the isoperimetric inequality in Cartan-Hadamard manifolds, and establishes a new comparison formula for total curvature of level sets.

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