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Results tagged with geometric-analysis
Search options questions only
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user 119114
3
votes
2
answers
425
views
Proof of Isoperimetric Inequality using Curve Shortening Flow
I am aware that there is a nice result where one uses curve shortening flow to prove the isoperimetric inequality on the Euclidean plane, but could not seem to find the original article where this was …
- 5,146
11
votes
1
answer
604
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Are there currently any plausible approaches to proving the Penrose сonjecture?
I have recently been reading some of the literature on the Penrose inequality, especially the papers by Bray and by Huisken and Ilmanen.
One notices immediately that the existing proofs for the Penro …
- 5,146
5
votes
1
answer
260
views
Neckpinch singularity of Ricci flow
I apologise if this question is unclear as I do not know much about the Ricci flow and am only asking out of curiosity. My understanding is that a neckpinch singularity is a local singularity in the …
- 5,146
5
votes
1
answer
331
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Ricci flow proof of isoperimetric inequality
It is well-known in geometric analysis that one can use curve-shortening flow to prove the isoperimetric inequality (where the general result requires curve-shortening flow for non-convex curves).
I …
- 5,146
1
vote
0
answers
104
views
Modelling fluid flows with mean curvature flow
A while ago I was wondering if the displacement of fluid described in this blog post
could be modelled with mean curvature flow or some other flow, but when I asked someone in Engineering they replied …
- 5,146
13
votes
2
answers
2k
views
Is there a solution of the Yamabe problem using Ricci flow?
Someone told me that it is possible to solve the Yamabe problem using Ricci flow. The proof I know of is the one originally proposed by Yamabe and then completed by Trudinger, Aubin and Schoen (in pa …
- 5,146
29
votes
2
answers
4k
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Formal mathematical definition of renormalization group flow
I was watching some lectures by Huisken where he mentioned that one-loop renormalization group flow was in some analogous to mean curvature flow. I have tried reading up the exact definition of what …
- 5,146