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Results tagged with mg.metric-geometry
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user 16702
Euclidean, hyperbolic, discrete, convex, coarse geometry, metric spaces, comparisons in Riemannian geometry, symmetric spaces.
8
votes
3
answers
1k
views
Brownian motion on Metric spaces
Is there a generalization of Brownian motion to general metric spaces (which should probably be length spaces)?
This should be a process satisfying
$$d(B_t, B_s) \sim \mathcal{N}(0, t-s)$$
and such t …
- 9,853
3
votes
When does heat kernel have both Gaussian upper and lower bounds?
I do not know much about the case of metric spaces, but for the heat kernel on a (noncompact) manifold without boundary, these estimates exist. There are various papers and book by Grigor`yan on that …
- 9,853
5
votes
2
answers
2k
views
Triangle area on surfaces of constant curvature
I am looking for an elementary derivation of the formula for the area of a geodesic triangle lying in a surface of constant curvature $\kappa$, depending on the angles and side length.
Of course, the …
- 9,853