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Results tagged with alexandrov-geometry
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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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Soul theorem for non-negativly curved open Alexandrov manifolds?
Alexandrov manifold means Alexandrov space which happens to be a manifold, i.e. the space of directions is homeomorphic to shpere. Sorry for introducing this new term.
For such a open manifold does t …
- 4,195
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Details of Perelman's example about soul of Alexandrov space
Reading Perelman's preprint(1991) Alexandrov space II now. Got confused about the last section 6.4, which contains an example which indicate that the statement ".... manifold is diffeomorphic to the n …
- 45k
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Is Level set of Regular functions in Alexandrov spaces again an Alex. space?
Let $X^n$ be an Alexandrov space, and $f: X^n\to \mathbb R^k$ a regular map, does the level set necessary be an Alexandrov space?
In my mind, the intrinsic metric on the level set is 'comparable' to …
- 45k