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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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Alexandrov spaces satisty $BE(K,N)$ and $BE(K,\infty)$?
Assume the Dirichlet form $\varepsilon$ adimits a Carre du champ $\Gamma$ and introduce the multilinear form $\Gamma_2$ $$
\Gamma_2 [f,g;\phi]:=\frac12 \int_X (\Gamma (f,g)L\phi -(\Gamma(f,Lg)+\Gamma( …
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curvature of subset of Alexandrov spaces
If M is a Riemannian manifold with $Ric \ge - \left( {n - 1} \right)$, $$ds_M^2 = d{t^2} + \exp \left( {2t} \right)ds_N^2$$ N is a submanifold of M. Then by Gauss-equation, we can prove $Ric\left( N …
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examples of space of direction at a point in an infinite dim Alexandrov space compact
The space of direction at a point in an infinite dim Alexandrov space can be compact?Please give examples or prove it's wrong.
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Must a hyperbolic cone over Riemannian manifold be manifold?
M is a hyperbolic cone over an n-1 dim Riemannian manifold N with $Ric(N) \ge - \left( {n - 2} \right)$ ie
$M = R \times {}_{\cosh \left( t \right)}N$,Surely N is an Alexandrov space,must M be a mani …
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Examples of Alexandrov spaces with sec>=-1 and first eigenvalue (n-1)^2/4
Could someone give examples of non-Riemannian manifolds that are Alexandrov spaces with $\mathrm{sec}\geq-1$ and the first eigenvalue equal to $(n-1)^2/4$?
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about parabolic cone
I want to prove some Alexandrov space M is parabolic cone X x R.Since Alex has no Riemannian metric,so how to do?Is there any (triangle) formula about the relation of distance of two points in M and d …
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Is level set of Busemann function on Alexandrov space again Alexandrov space?
M is an Alexandrov space with curv>=-1,containing a line(ray).Is level set of Busemann function on M again Alexandrov space?If not,can you give a counterexample?
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examples of totally geodesic subset
Could you give examples of totally geodesic subset of codim>1 in positively curved Alexandrov space?
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a result of soul theorem,right?
$X$ is an $n$-dim positively curved manifold and $Y$ is a totally geodesic submanifold of codimension 1. Then cutting along $Y$ we get $n$-dim positively curved manifolds without boundary, by soul the …
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positively curved Alexandrov space
I heard a conjecture "3-dim positively curved Alexandrov space is of the form S^3/J.(I cannot make sure my statement is accurate).
What is the classification of n-dim positively curved Alexandrov spac …
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Extend the Wilking Connectiveity Theorem to Alexandrov spaces
In the conference "on Manifolds with Non-negative Sectional Curvature" held in 2007,
Problem 6 is:
Extend the Wilking Connectivity Theorem to Alexandrov spaces, i.e. if $X$ is a positively curved …
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3-dim positively curved Alexandrov space
What is the classification of 3-dim positively curved Alexandrov space?
And if a 3-dim positively curved Alexandrov space has a totally (quasi)geodesic subset,then the classification?
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