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552 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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0answers
123 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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65 views

Functional involving Ricci curvature: convex and coercive?

Let $(M,g)$ be a Riemannian manifold with Levi-Civita connection $\nabla$, volume form $\mu_g$, and Ricci curvature $\text{Rc}_g$. Question: Given a fixed vector field $V\in\Gamma(TM)$, under what ...
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101 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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169 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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147 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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204 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 ...