• Title/Summary/Keyword: holomorphic flows

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TOPOLOGICAL CLASSIFICATION OF ω-LIMIT SETS OF HOLOMORPHIC FLOWS ON ℂ1

  • Choy, Jaeyoo;Chu, Hahng-Yun
    • Journal of the Chungcheong Mathematical Society
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    • v.22 no.1
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    • pp.73-80
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    • 2009
  • This paper aims to study local and global structure of holomorphic flows on $\mathbb{C}^1$. At a singular point of a holomorphic flow, we locally sector the flow into parabolic or elliptic types. By the local structure of holomorphic flows, we classify all the possible types of topologies of $\omega$-limit sets.

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RELATIVE TWISTED KÄHLER-RICCI FLOWS ON FAMILIES OF COMPACT KÄHLER MANIFOLDS

  • Choi, Young-Jun
    • East Asian mathematical journal
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    • v.37 no.5
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    • pp.577-584
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    • 2021
  • Let p : X → D be a proper surjective holomorphic submersion where X is a Kähler manifold and D is the unit disc in ℂ. Let Ω be a d-closed semi-positive real (1, 1)-form on X. If each Xs := p-1(s) for s ∈ D satisfies $-c_1(X_s)+{\Omega}{\mid}_{X_s}$ is Kähler, then the Kähler-Ricci flow twisted by ${\Omega}{\mid}_{X_s}$ has a long time solution by Cao's theorem. This family of twisted Kähler-Ricci flows induces a relative Kähler form ω(t) on the total space X. In this paper, we prove that the positivity of ω(t) is preserved along the twisted Kähler-Ricci flow.