CD meets CAT

Vitali Kapovitch; Christian Ketterer

CD meets CAT

Differential Geometry 2018-01-23 v3 Metric Geometry

Authors: Vitali Kapovitch , Christian Ketterer

Abstract

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

Keywords

general topology

Cite

@article{arxiv.1712.02839,
  title  = {CD meets CAT},
  author = {Vitali Kapovitch and Christian Ketterer},
  journal= {arXiv preprint arXiv:1712.02839},
  year   = {2018}
}

Comments

We add a new section where we prove a new theorem that if a $CD(K,n)$ space with finite $n$ has curvature bounded above then it is infinitesimally Hilbertian. Using this we remove the infinitesimal Hilbertianness assumption from the main theorem. Minor corrections, additional references

CD meets CAT

Abstract

Keywords

Cite

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