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arXiv · 2607.12842

Lectures on Alexandrov spaces with curvature bounded below

Vitali Kapovitch·Nina Lebedeva·Anton Petrunin
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Abstract

An introduction to Alexandrov spaces with curvature bounded below. Topics include various comparison conditions, the globalization theorem, tangent spaces and spaces of directions, gradient flows, the splitting theorem, dimension and volume, Gromov's selection theorem, the boundary and the doubling theorem, and quotient spaces. We also give a brief overview of the two-dimensional theory, the main precursor to modern Alexandrov geometry.

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Vitali Kapovitch, Nina Lebedeva, Anton Petrunin. 2026-07-14. Lectures on Alexandrov spaces with curvature bounded below. https://arxiv.org/abs/2607.12842

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