As on arXiv
Abstract
This paper investigates the twisted Calabi functional and the associated twisted Calabi flow on compact Kähler manifolds. Our main contributions are threefold: first, we establish the convexity of the twisted Calabi functional at its critical points; second, we prove the short-time existence of the twisted Calabi flow; and third, we demonstrate the stability of this flow in the neighborhood of twisted constant scalar curvature Kähler metrics. These results provide an analytic foundation for studying the twisted Calabi flow and resolve questions about its local behavior.
Its neighbourhood
Connected papers
The 8 papers on this site closest to this one, judged by the topics they share, the words and phrases in their titles and abstracts, and their authors. They are not its citations, but a map of the work around it. Papers here go back to 2021, plus the canon.
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Existence of twisted Calabi flow and deformation from the -flow to Calabi flow
Topics Kähler–Einstein & K-stability, Scalar curvature, Other curvature flows · Same authors Jie He, Haozhao Li · Shared terms “twisted Calabi”, “Calabi flow”, “time existence”
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Calabi flow with bounded scalar curvature (II)
Topics Kähler–Einstein & K-stability, Scalar curvature, Other curvature flows · Same author Haozhao Li · Shared terms “Calabi flow”, “compact Kähler”
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Hermitian Calabi functional in complexified orbits
Topics Kähler–Einstein & K-stability, Other curvature flows, Kähler geometry · Same author Jie He · Shared terms “Calabi functional”, “Calabi flow”, “critical points”
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Calabi flow with bounded scalar curvature
Topics Kähler–Einstein & K-stability, Scalar curvature, Other curvature flows · Same author Haozhao Li · Shared terms “Calabi flow”
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Long-time existence of the Calabi flow on Kähler surfaces with bounded Sobolev constants
Topics Kähler–Einstein & K-stability, Other curvature flows, Kähler geometry · Same author Haozhao Li · Shared terms “Calabi flow”, “compact Kähler”, “time existence”
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Pseudo-Calabi Flow on Toric Variety
Topics Kähler–Einstein & K-stability, Scalar curvature, Other curvature flows · Shared terms “Calabi flow”, “constant scalar”, “time existence”
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The Ricci iteration towards cscK metrics
Topics Kähler–Einstein & K-stability, Scalar curvature, Other curvature flows · Shared terms “Calabi flow”, “constant scalar”, “Kähler metrics”
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An improvement of regularity result for pseudo Calabi flow
Topics Kähler–Einstein & K-stability, Other curvature flows, Kähler geometry · Shared terms “Calabi flow”, “time existence”
Read around it
Background reading
The guides for the topics of this paper: what each idea is, why it matters, and the papers to read first.
In the guidebook
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The 3-sphere, lens spaces, the Poincaré sphere, the Hopf fibration and the shape of space.
- 10A.2Finite Rotation Groups and Spherical Space Forms
Klein's classification by counting poles, the binary groups, and every quotient of the round 3-sphere.
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Spheres mapped into manifolds: the algebraic topology that finite extinction runs on.