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arXiv · 1712.02839

CD meets CAT

Vitali Kapovitch·Christian Ketterer
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Abstract

We show that if a noncollapsed $CD(K,n)$ space $X$ with $n\ge 2$ has curvature bounded above by $κ$ in the sense of Alexandrov then $K\le (n-1)κ$ and $X$ is an Alexandrov space of curvature bounded below by $K-κ(n-2)$. We also show that if a $CD(K,n)$ space $Y$ with finite $n$ has curvature bounded above then it is infinitesimally Hilbertian.

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Vitali Kapovitch, Christian Ketterer. 2018-01-20. CD meets CAT. https://arxiv.org/abs/1712.02839

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