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Weakly noncollapsed RCD spaces with upper curvature bounds

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arxiv 1901.06966 v1 pith:AAR5AACI submitted 2019-01-21 math.DG math.MG

Vitali Kapovitch , Christian Ketterer This is my paper · ORCID
classification math.DGmath.MG
keywords curvatureabovealexandrovboundedboundsconstkappamathcal
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abstract

We show that if a $CD(K,n)$ space $(X,d,f\mathcal{H}^n)$ with $n\geq 2$ has curvature bounded from above by $\kappa$ in the sense of Alexandrov then $f=const$.

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  1. On the structure of RCD spaces with upper curvature bounds

    math.DG 2019-08 accept novelty 8.0 of 10

    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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