Generalized Lagrangian mean curvature flows in almost Calabi-Yau manifolds

TL;DR

This paper investigates the behavior of generalized Lagrangian mean curvature flows in almost Calabi-Yau manifolds, revealing singularity characteristics and convergence to special Lagrangian cones, with implications for flow singularities.

Contribution

It introduces a characterization of singularities and convergence properties of the flow in almost Calabi-Yau manifolds, extending previous understanding of Lagrangian mean curvature flows.

Findings

Singularities are characterized by the second fundamental form.

Rescaled flow converges to special Lagrangian cones.

No finite time Type-I singularities occur for zero-Maslov class flows.

Abstract

In this paper, we study the generalized Lagrangian mean curvature flow in almost Einstein manifold proposed by T. Behrndt. We show that the singularity of this flow is characterized by the second fundamental form. We also show that the rescaled flow at a singularity converges to a finite union of Special Lagrangian cones for generalized Lagrangian mean curvature flow with zero-Maslov class in almost Calabi-Yau manifold. As a corollary, there is no finite time Type-I singularity for such a flow.