Singularity formation along the line bundle mean curvature flow

2023/10/26 by Yu Hin Chan, Chan, Yu Hin, Adam K. Jacob +1 · 1 citation
Mathematics · Physics and Astronomy · #Black Holes and Theoretical Physics #Differential Geometry (math.DG) #FOS: Mathematics #Geometric Analysis and Curvature Flows #Geometry and complex manifolds

paper · pdf · doi:10.48550/arxiv.2310.17709

openalex publication_date 2023/10/26 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

Abstract

The line bundle mean curvature flow is a complex analogue of the mean curvature flow for Lagrangian graphs, with fixed points solving the deformed Hermitian-Yang-Mills equation. In this paper we construct two distinct examples of singularities along the flow. First, we find a finite time singularity, ruling out long time existence of the flow in general. Next we show long time existence of the flow with a Calabi symmetry assumption on the blowup of \mathbb Pⁿ, n≥ 3, if one assumes supercritical phase. Using this, we find an example where a singularity occurs at infinite time along the destabilizing subvariety in the semi-stable case.

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