Stability of the Type IIA flow and its applications in symplectic geometry
Teng Fei, Duong H. Phong, Sebastien Picard, and Xiangwen Zhang
TL;DR
This paper proves the dynamical stability of the Type IIA flow near Ricci-flat Kähler metrics on Calabi-Yau 3-folds and applies this to show stability of the Kähler property under symplectic deformations.
Contribution
It establishes the stability of the Type IIA flow near stationary points and applies this to symplectic deformation stability of Calabi-Yau 3-folds.
Findings
Type IIA flow is dynamically stable near Ricci-flat Kähler metrics.
Stability under symplectic deformations of the Kähler property for Calabi-Yau 3-folds.
Provides a new approach to understanding geometric stability in symplectic geometry.
Abstract
In this paper the dynamical stability of the Type IIA flow with no source near its stationary points is established. These stationary points had been shown previously by the authors to be Ricci-flat K\"ahler metrics on Calabi-Yau 3-folds. The dynamical stability of the Type IIA flow is then applied to prove the stability under symplectic deformations of the K\"ahler property for Calabi-Yau 3-folds.
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Taxonomy
TopicsGeometry and complex manifolds · Geometric Analysis and Curvature Flows · Algebraic Geometry and Number Theory