# Questions tagged [kahler-ricci-flow]

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

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### Vanishing components of Kähler metric

Let $(X, \omega)$ be a $n$-dimensional complex Kähler manifold such that $\omega^{n-1}=d\alpha$. Does $\partial\alpha^{n-1,n-2} =0$ (resp. $\bar\partial\alpha^{n-2,n-1} =0$) Where $\alpha^{n-1,n-2}$ ...
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### Reference request: a PDE related to Kahler–Ricci flow

I was reading the survey by Imbert and Silvestre where I noticed the PDE $$\frac {\partial u} {\partial t} = \ln(\det (D^2u))$$ for the study of the Kahler–Ricci flow (Eq (2.2) at page 10 in ... 75 views

### Upper bound on the bisectional curvature

This is a follow-up to the question Schwarz lemma and bisectional curvature lower bound. Looking at the same note Song and Weinkove - Lecture notes on the Kähler–Ricci flow, page 24, the first line ...
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Reading a proof of the Schwarz lemma for the Kähler-Ricci flow from p22 of these lecture notes. I am confused as to what they mean by taking $$\inf _{x \in M} \{\hat{R}_{i \bar i j \bar j}(x) \mid \{\... 4 votes 2 answers 505 views ### Reading material for an analytical aspect of Kähler Geometry This question was originally posted on MSE. But I would like to post it here to see whether anyone could recommend some reference for me. I am currently reading the paper "Three-circle theorem ... 9 votes 1 answer 433 views ### Ricci flow preserves almost Kahler condition? I have been unable to find a reference to the following (perhaps too naive) question. Suppose we have an almost Kahler manifold (M^{2n},\omega,J,g) i.e. the almost complex structure J is non-... 5 votes 0 answers 148 views ### reference for the weak compactness of currents I am trying to follow the arguments in page 22 of the following paper k\"{a}hler currents and null loci It quotes the weak compactness of currents, I wonder if there is any reference about it. My ... 1 vote 0 answers 96 views ### Ricci flow preserves locally symmetry along the flow Let (M,g_0) be a closed locally symmetric Riemannian manifold and let g(t)_{t\in[0,T)} be a solution to the Ricci flow on M with g(0)=g_0. How one can prove that Ricci flow preserves locally ... 2 votes 0 answers 89 views ### Extending Kahler metric across a divisor Let (X,\omega) be a complete noncompact Kahler manifold of finite volume. Suppose X is can be compactified to a compact projective manifold M so that D=M-X is a divisor of simple normal ... 2 votes 0 answers 517 views ### Tian's approach for solving the conjecture of invariance of plurigenera in Kahler setting Let f:X\to Y be a smooth holomorphic fibre space whose fibres f^{-1}(y) have pseudoeffective canonical bundles. suppose that$$\frac{\partial \omega(t)}{\partial t}=-Ric_{X/Y}(\omega(t))-\omega(... 