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arXiv · 1809.00603

Uniform boundedness on extremal subsets in Alexandrov spaces

Tadashi Fujioka
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Abstract

In this paper, we study extremal subsets in Alexandrov spaces with dimension $n$, curvature $\geκ$, and diameter $\le D$. We show that the following three quantities are uniformly bounded above in terms of $n$, $κ$, and $D$: (1) the number of extremal subsets in an Alexandrov space; (2) the Betti numbers of an extremal subset; (3) the volume of an extremal subset. The proof is an application of essential coverings introduced by Yamaguchi.

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Tadashi Fujioka. 2024-11-21. Uniform boundedness on extremal subsets in Alexandrov spaces. https://doi.org/10.1007/s12220-024-01864-7

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