Hamiltonian F-Stability of Complete Lagrangian Self-Shrinkers

In this paper, we study the Lagrangian F-stability and Hamiltonian F-stability of Lagrangian self-shrinkers. We prove a characterization theorem for the Hamiltonian F-stability of n-dimensional complete Lagrangian self-shrinkers without boundary, with polynomial volume growth and with the second fundamental form satisfying the condition that there exist constants C0>0\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$C_0>0$$\end{document} and ε<116n\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$\varepsilon <\frac{1}{16n}$$\end{document} such that |A|2≤C0+ε|x|2\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$|A|^2\le C_0+\varepsilon |x|^2$$\end{document}. We characterize the Hamiltonian F-stability by the eigenvalues and eigenspaces of the drifted Laplacian.