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Results tagged with ricci-flow
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user 1540
3
votes
Bryant Soliton is asymptotically cylindrical?
One method is to repeat in dimensions $n$ Bryant's analysis in which he proves the existence and uniqueness of the so called Bryant soliton in $3$-dimensions: http://www.math.duke.edu/~bryant/3DRotSym …
- 7,197
8
votes
A simple and good reference about solitons
The answers so far seem to be about "solitons" in general which just means a "self similar solution to some PDE." Ricci solitons meet this criteria, but in case you'd like more Ricci soliton focused m …
- 7,197
6
votes
Ricci flow descending from an universal cover
I was going to post this as a comment, but it got too long. I'm not exactly sure how to answer the question as written, but the following might be enlightening:
A crucial piece of information for your …
- 7,197
3
votes
Hamilton-Ivey pinching in dimension 4
One striking example of the failure of Hamilton-Ivey pinching can be seen here in which it is shown that the FIK shrinkers (which do not have non-negative Ricci curvature, much less non-negative secti …
- 7,197
8
votes
Accepted
the left hand side of the Ricci flow equation at the initial value
Misha's comment could be a bit misleading. In particular, it is not true that the Ricci flow should exist on a slightly bigger interval $(-\epsilon,T)$ with $g(0) = g_0$. One way to see this is by thi …
- 7,197
11
votes
Ricci flow and isometry group
The answer is yes (I'm assuming you are asking about closed manifolds, non-compactness allows for all sort of crazy things to happen, you can check out the work of Topping and collaborators).
Kotsch …
- 7,197
5
votes
Exponential convergence of Ricci flow
See Struwe, Curvature Flows on Surfaces. http://www.numdam.org/item/ASNSP_2002_5_1_2_247_0/, Section 6.2, (particularly equation (64) and surrounding text) where he uses the Kazdan-Warner identity to …
- 7,197
9
votes
Accepted
Ricci flow negative curvature
The answer to your first question is Yes. The equation
$$
\tag{*} \partial_t g = -2\textrm{Ric} - 2(n-1)g
$$
is a Ricci flow type equation that admits hyperbolic space as a static solution. In fact, i …
- 7,197