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Results tagged with alexandrov-geometry
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user 90512
Alexandrov geometry studies non smooth analogues of Riemannian manifolds with curvature bounded from below or above. It includes spaces with curvature bounded below (briefly $\mathrm{CBB}[\kappa]$) and spaces with curvature bounded above (briefly $\mathrm{CAT}[\kappa]$).
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Can we realize the smooth metric of an Alexandrov space with nonnegative curvature by a Riem...
We know that a smooth Riemannian manifold with nonnegative curvature is an Alexandrov space (with induced metric) of nonnegative curvature.
What about the converse? That is, given a smooth metric d o …
- 1,799
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If M times circle admits a locally CAT(0)-metric, then M also carries a locally CAT(0)-metric?
A locally CAT(0) metric on length space means that every point in it has a geodesically convex neighborhood such that every triangle in it is slimmer than the comparison triangle in the Euclidean plan …
- 1,799