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arXiv · 1701.04725

Differential Inequalities for Distance Comparison

Murat Limoncu·Şahin Koçak
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Abstract

Comparison of $1$-dimensional distance functions is a basic tool in Alexandrov geometry and it is used to characterize spaces with curvature bounded above or below. For the zero curvature bound there is a differential inequality which enables one to check this comparison directly on a given smooth $1$-dimensional distance function. In this note we give a generalization of this property to arbitrary curvature bounds.

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Murat Limoncu, Şahin Koçak. 2017-01-17. Differential Inequalities for Distance Comparison. https://arxiv.org/abs/1701.04725

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