Hamiltonian L-stability of Lagrangian Translating Solitons

TL;DR

This paper investigates the stability properties of Lagrangian translating solitons under Hamiltonian variations, establishing that all such solitons are Hamiltonian L-stable through variation formula analysis.

Contribution

It provides the first and second variation formulas for the F-functional and proves the universal Hamiltonian L-stability of Lagrangian translating solitons.

Findings

All Lagrangian translating solitons are Hamiltonian L-stable.

Derived explicit first and second variation formulas for the F-functional.

Established stability results in the context of translating solitons.

Abstract

In this paper, we compute the first and second variation formulas for the F-functional of translating solitons and study the Hamiltonian L-stability of Lagrangian translating solitons. We prove that any Lagrangian translating soliton is Hamiltonian L-stable.