# Questions tagged [kahler-ricci-flow]

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

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### 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 ...

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### 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(...

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### 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!

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### 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 ...