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Results tagged with infinite-dimensional-manifolds
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user 766
33
votes
Are infinite dimensional constructions needed to prove finite dimensional results?
In his famous proof of the Poincare conjecture, Perelman heuristically derived a key monotonicity formula for finite-dimensional Ricci flow, by interpreting this flow as a renormalised version of an i …
- 114k
19
votes
Ricci Curvature in infinite dimensions?
There is a paper of Lott and Villani that defines the concept of nonnegative Ricci curvature in an arbitrary measured length space:
http://math.berkeley.edu/~lott/LottVillani.pdf
There is a dimensio …
- 114k