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Results tagged with alexandrov-geometry
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user 6094
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 $\mathrm{CAT}[\kappa]$).
11
votes
4
answers
730
views
Source for: Geodesics in CAT(0) spaces
I am seeking a good introductory reference that could lead to an understanding of
the properties of geodesics in
complete CAT(0) metric spaces.
I am especially interested in learning the differences b …
- 45k
17
votes
1
answer
525
views
Is $\partial X$ a sphere for $X$ a complete CAT$(0)$ space?
Let $X$ be a complete CAT$(0)$ metric space, and $\partial X$ its boundary.
One way to define $\partial X$ is as the equivalence class of geodesic rays
$\gamma(t), \gamma'(t)$
that remain within a co …
- 63.9k
6
votes
2
answers
385
views
Are shortest halving curves simple closed geodesics?
Let $S$ be a smooth convex surface in $\mathbb{R}^3$
(although my question may as well be asked for the surface of a polyhedron).
Say that $\gamma$ is a shortest halving curve if
(a) it partitions the …
- 151k