Translating solitons to symplectic and Lagrangian mean curvature flows

TL;DR

This paper constructs finite blow-up examples for symplectic mean curvature flows and analyzes properties of symplectic translating solitons, revealing a lower bound on the Kähler angle related to the translation direction.

Contribution

It introduces finite blow-up examples and establishes a new inequality involving the Kähler angle for symplectic translating solitons.

Findings

Constructed finite blow-up examples for symplectic mean curvature flows.

Proved a lower bound for the Kähler angle of symplectic translating solitons.

Linked the Kähler angle bound to the translation direction vector.

Abstract

In this paper, we construct finite blow-up examples for symplectic mean curvature flows and we study properties of symplectic translating solitons. We prove that, the K\"ahler angle $\alpha$ of a symplectic translating soliton with $\max |A|=1$ satisfies that $\sup |\alpha|>\frac{\pi}{4}\frac{|T|}{|T|+1}$ where $T$ is the direction in which the surface transltes.