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Results tagged with mg.metric-geometry
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user 69441
Euclidean, hyperbolic, discrete, convex, coarse geometry, metric spaces, comparisons in Riemannian geometry, symmetric spaces.
8
votes
2
answers
4k
views
Metric measure spaces: in what sense is analysis on these spaces "non-smooth"
I understand the basic definition of a metric measure space to be the following:
A metric measure space is a triple of a space $X$, metric $d$, and measure $m$: $(X,d,m)$ in the sense that the met …
- 427
4
votes
1
answer
181
views
Domains in $\mathbb{R}^n$ for which Hajlasz-Sobolev spaces and Sobolev Spaces are the same
I'm reading Heinonen's book on metric measure spaces. He writes that for general domains $\Omega \subset \mathbb{R}^n$, $M^{1,p}(\Omega) \subset W^{1,p}(\Omega)$ where the former are Hajlasz-Sobolev s …
- 427