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Results tagged with calculus-of-variations
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user 1345
Questions on the calculus of variations, which deals with the optimization of functionals mostly defined on infinite dimensional spaces.
6
votes
Accepted
Ricci flow proof of isoperimetric inequality
Anthony Manning proved that the volume entropy decreases under volume normalized Ricci flow on surfaces of negative curvature. Question 4 at the end of his paper asks whether the Cheeger isoperimetric …
- 66.2k
12
votes
Accepted
A riemannian manifold with finitely many closed contractible geodesics
I think if you take the metric on $\mathbb{R}^2$ obtained by rotating a curve which is $\sqrt{1-x^2}$ for $-1\leq x\leq 0$, and $x^2+1$ for $x\geq 0$ around the $x$-axis, then I think there will be a …
- 66.2k
4
votes
Accepted
Do there exist any variational principles on the space of braids (or knots)?
O'Hara introduced knot energies, and a Möbius invariant case was studied by Freedman-He-Wang. For prime knots, Zheng-Xu He subsequently showed that there exists a smooth minimizer (up to Möbius transf …
- 66.2k