As on arXiv
Abstract
Let be a compact symplectic manifold. We denote by the space of all almost complex structure compatible with . has a natural foliation structure with the complexified orbit as leaf. We obtain an explicit formula of the Hessian of Hermitian Calabi functional at an extremal almost Kähler metric in . We prove that the Hessian of Hermitian Calabi functional is semi-positive definite at critical point when restricted to a complexified orbit, as corollaries we obtain some results analogy to Kähler case. We also show weak parabolicity of the Hermitian Calabi flow.
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.
-
Twisted Calabi functional and twisted Calabi flow
Topics Kähler–Einstein & K-stability, Other curvature flows, Kähler geometry · Same author Jie He · Shared terms “Calabi functional”, “Calabi flow”, “critical points”
-
Calabi flow with bounded scalar curvature
Topics Kähler–Einstein & K-stability, Other curvature flows, Kähler geometry · Same author Kai Zheng · Shared terms “Calabi”, “extremal”
-
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 Kai Zheng · Shared terms “Calabi”
-
Pseudo-Calabi Flow on Toric Variety
Topics Kähler–Einstein & K-stability, Other curvature flows, Kähler geometry · Same author Kai Zheng · Shared terms “Calabi”
-
Existence of twisted Calabi flow and deformation from the -flow to Calabi flow
Topics Kähler–Einstein & K-stability, Other curvature flows, Kähler geometry · Same author Jie He · Shared terms “Calabi”
-
Calabi flow with bounded scalar curvature (II)
Topics Kähler–Einstein & K-stability, Other curvature flows, Kähler geometry · Shared terms “Calabi”
-
On global Chern-Calabi flows on compact complex surfaces
Topics Kähler–Einstein & K-stability, Other curvature flows, Kähler geometry · Shared terms “Calabi”, “extremal”, “Hermitian”
-
Semistability and asymptotics of geometric flows
Topics Kähler–Einstein & K-stability, Other curvature flows, Kähler geometry · Shared terms “Hermitian”, “Calabi”
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.