Questions tagged [kahler-ricci-flow]

Kähler-Ricci flow is a Kähler version of Ricci-flow for Kähler manifolds

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2answers
230 views

Reading material for an analytical aspect of Kähler Geometry

This question was originally posted on MSE. But I would like to post it here to see whether anyone could recommend some reference for me. I am currently reading the paper "Three-circle theorem ...
9
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1answer
359 views

Ricci flow preserves almost Kahler condition?

I have been unable to find a reference to the following (perhaps too naive) question. Suppose we have an almost Kahler manifold $(M^{2n},\omega,J,g)$ i.e. the almost complex structure $J$ is non-...
5
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0answers
105 views

reference for the weak compactness of currents

I am trying to follow the arguments in page 22 of the following paper k\"{a}hler currents and null loci It quotes the weak compactness of currents, I wonder if there is any reference about it. My ...
1
vote
0answers
86 views

Ricci flow preserves locally symmetry along the flow

Let $(M,g_0)$ be a closed locally symmetric Riemannian manifold and let $g(t)_{t\in[0,T)}$ be a solution to the Ricci flow on $M$ with $g(0)=g_0$. How one can prove that Ricci flow preserves locally ...
2
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0answers
73 views

Extending Kahler metric across a divisor

Let $(X,\omega)$ be a complete noncompact Kahler manifold of finite volume. Suppose $X$ is can be compactified to a compact projective manifold $M$ so that $D=M-X$ is a divisor of simple normal ...
2
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0answers
446 views

Tian's approach for solving the conjecture of invariance of plurigenera in Kahler setting

Let $f:X\to Y$ be a smooth holomorphic fibre space whose fibres $f^{-1}(y)$ have pseudoeffective canonical bundles. suppose that $$\frac{\partial \omega(t)}{\partial t}=-Ric_{X/Y}(\omega(t))-\omega(...
5
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2answers
410 views

Ricci flow on Kähler manifold

Knowing the Ricci flow on Riemann surfaces, see e.g. Ricci flow on Riemann surfaces How could we write the Ricci flow on Kähler manifold? Thanks for the reply!
2
votes
2answers
451 views

Curvatures preserved under the Kahler-Ricci flow

Maybe it is a trivial question. Is there any obvious reason that non-negative holomorphic bisectional curvature is preserved by (normalized) Kahler-Ricci flow, but non-negative Ricci curvature is not ...