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CD meets CAT
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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 $\kappa$ 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.
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Cited by 1 Pith paper
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On the structure of RCD spaces with upper curvature bounds
Every RCD space with curvature bounded above is a topological manifold with boundary whose interior is the regular set, a smooth geodesically convex manifold.
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