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Singularity Formation along the Line Bundle Mean Curvature Flow
- Chan, Yu Hin
- Advisor(s): Jacob, Adam
Abstract
The line bundle mean curvature flow is a complex analogue of the mean curvature flow forLagrangian 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 P^n, 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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