Collapsing of the line bundle mean curvature flow on Kähler surfaces

2019/12/31 by Takahashi, Ryosuke
#Differential Geometry (math.DG) #FOS: Mathematics #Primary 53C55 #Secondary 53C44

paper · doi:10.48550/arxiv.1912.13145

Abstract

We study the line bundle mean curvature flow on Kähler surfaces under the hypercritical phase and a certain semipositivity condition. We naturally encounter such a condition when considering the blowup of Kähler surfaces. We show that the flow converges smoothly to a singular solution to the deformed Hermitian-Yang-Mills equation away from a finite number of curves of negative self-intersection on the surface. As an application, we obtain a lower bound of a Kempf-Ness type functional on the space of potential functions satisfying the hypercritical phase condition.

Related

• Singularity formation along the line bundle mean curvature flow
• Weak limits of the J-flow and the deformed Hermitian-Yang-Mills flow on Kähler surfaces: boundary cases
• Stability of line bundle mean curvature flow
• Convergence properties of the Yang-Mills flow on Kaehler surfaces
• On the tangent flow to the collapsing Kähler-Ricci flow on Hirzebruch surfaces