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Results tagged with alexandrov-geometry
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user 28128
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 $\mathrm{CAT}[\kappa]$).
10
votes
Gromov-Hausdorff limits of 2-dimensional Riemannian surfaces
Consider a shortest closed geodesic $\gamma$ on the surface of length sys, and the normal exponential map of $\gamma$. Using the lower curvature bound, we obtain an upper bound on the total area as $\ …
- 16.6k
4
votes
Accepted
Fundamental group of Alexandrov space.
Under these hypotheses the systole of $X$ is clearly bounded from below, and the usual comparison arguments would give an upper bound on the number of points in an $\epsilon$-net in $X$. Then every l …
- 16.6k
3
votes
Accepted
Convexity of set of normal directions in a CAT(0)-space
This is not true even at an ordinary conical singularity with total angle greater than $2\pi$ on a surface.
- 16.6k