The ricci-flow tag has no usage guidance.

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### Optimal exponent in the Lojasiewicz-Simon gradient inequality

Lojasiewicz's theorem asserts that if $F: \mathbb{R}^n\to \mathbb{R}$ is a real-analytic function in a neighborhood of its critical point $0$, then there exist constants $\theta\in (0,1/2]$, ...

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334 views

### 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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91 views

### 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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133 views

### 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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586 views

### 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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90 views

### 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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139 views

### 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 ...

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50 views

### 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, ...

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59 views

### 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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126 views

### Ricci flow on non-compact manifold

Suppose $\omega$ defines a Kähler metric on a non-compact complex manifold. Does
the Kähler-Ricci flow equation always have a solution (for small $t$)?

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203 views

### RG flow and Ricci flow

It looks like the Laplace operator in the nonlinear sigma model (say the Polyakov action) is different from the Laplace-Beltrami operator, how can one get the Ricci flow as a low order approximation ...

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170 views

### Isoperimetric profile

In the paper of Andrews and Bryan Curvature bounds by isoperimetric comparison for normalized Ricci flow on the two-sphere http://arxiv.org/abs/0908.3606, the isoperimetric profile is defined by ...

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225 views

### A question from Hamilton's Ricci Flow book by bennett chow

On page 3 of the book before exercise 1.2, is written: "torsion free is a compatibility condition with the differentiable structure". I correctly do not understand how torsion-free condition results ...