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Results tagged with mg.metric-geometry
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user 100163
Euclidean, hyperbolic, discrete, convex, coarse geometry, metric spaces, comparisons in Riemannian geometry, symmetric spaces.
6
votes
1
answer
230
views
Reference request: acceleration/curvature of curve in metric space
Let $(X,d)$ be a metric space. Given a continuous curve $\gamma_t : [0,1] \rightarrow X$, the metric speed is defined by $$ |\gamma_t^\prime | := \lim_{s\rightarrow t} \frac{d(\gamma_s, \gamma_t)}{|t- …
- 660
1
vote
0
answers
54
views
Lax CD(K, $\infty)$ space in the sense of Sturm
In K.T. Sturm's "On the geometry of metric measure spaces. I", Definition 4.5, he introduces a "lax" version of the usual CD(K,$\infty$) lower bound. Namely, one allows for $\epsilon$-approximate leng …
- 660
1
vote
1
answer
259
views
Wasserstein space with strictly non-positive sectional curvature
Let $(X,d)$ be a (separable, complete) metric space with uniformly strictly non-positive curvature in the sense of Alexandrov, i.e. $(X,d)$ satisfies a $CAT(K)$ inequality for some $K<0$.
Does it hold …
- 660
0
votes
0
answers
343
views
Isometry group of a complete separable metric space is Polish?
Let $(X,d)$ be a complete separable metric space, and endow $Iso(X,d)$ with the pointwise convergence topology.
I've seen a few sources say this is clearly a Polish group, but why is this this the c …
- 660