# Tagged Questions

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### Prerequisites for reading Gregory Perelman's work

What are the prerequisites for understanding the work of Perelman concerning the Poincaré conjecture? I am referring to the last three papers here.
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### Faster (than normal) convergence of the normalized Ricci flow on surfaces

Consider a compact surface $M$ of genus $\gamma > 1$ (I am using the more usual letter "$g$" to denote metric), and the normalized Ricci flow on it. It is known that at time $t$, the scalar ...
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### ricci flow on surfaces

In Hamiltons paper "Ricci flow on surfaces" there is an estimate on $|\nabla R|^2$ which shows that $|\nabla R|^2 \leq C_1 \exp{\frac{rt}{2}}$ for some constant $C_1$. Actually for any solution of the ...
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### On Perelman's paper

In section 5 in "The entropy formula for the Ricci flow and its geometric applications" Grisha Perelman has written: Fix a closed manifold $M$ with a probability measure $m$, and suppose that our ...
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### Ricci soliton on contact manifolds

Recently I am studying Ricci flow and its self-similar solution called Ricci soliton. In this respect I found some papers which focuses Ricci soliton in the setting of various kind of contact ...
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### Sources on evolution of submanifolds subject to Ricci flow

I am seeking any textbook or paper addressing the evolution of submanifolds of a manifold undergoing Ricci Flow. Please, any pointer towards this topic is more than welcome. This old MO post may be ...
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### Variational Properties of the Perelman Functional

After reading a bit more about Perelman's entropy and gradient solitons, I came up with a hunch, which I must test. Non-singular solitons can be regarded as critical points of Perelman's entropy, or ...
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### Expressing the Ricci flow as a gradient flow in a case that manifold $(M,g)$ is a Riemannian manifold with boundary

I want to express the Ricci flow as a gradient flow in a case that manifold $(M,g)$ is a Riemannian manifold with boundary. For this I use the Einstein-Hilbert action S(g_{\mu \nu})=\frac{1}{16\pi}\...
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### Example of steady Ricci soliton whith indefinite or nonpositive Ricci curvature

I am looking for example of steady Ricci soliton with indefinite or nonpositive Ricci curvature. Any help will be appreciated. Thanks!
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### Two questions about Li-Yau-Hamilton estimate

This question is from my question on mathematics. Picture below is from 231 page . For to prove $Q\ge 0$ on $M \times (0,T)$, $(\partial_t -\Delta)Q \ge 0$ and $Q\ge 0$ are needed to prove.But I ...
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### Derivation of an expression in the Ricci flow on surfaces

Recently I am studying Benett Chow and Dan Knopf's book titled Ricci flow: An Introduction. In Chapter 5 (Ricci flow on surfaces), I am stuck in a straightforward deduction. Maybe it is very simple, ...