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Results tagged with alexandrov-geometry
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user 4354
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 $\mathrm{CAT}[\kappa]$).
17
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3
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Is there Domain Invariance for Alexandrov spaces?
A colleague asked me this question recently. Every injective continuous map between manifolds of the same (finite) dimension is open - this is Brouwer's Domain Invariance Theorem. Is the same true for …
- 32.4k
11
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1
answer
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In a locally CAT(k) space, does uniqueness of geodesics imply the lack of conjugate points?
A complete, simply connected Riemannian manifold has no conjugate points if and only if every geodesic is length-minimizing. I just realized that I don't know whether the same is true for a locally CA …
- 32.4k