A closed Lagrangian $L$ in ${\mathbin{\mathbb{C}}}^{m}$ is called an LMCF expander if $H=\alpha F^{\perp}$ in $C^{\infty}(T{\mathbin{\mathbb{C}}}^{m}|_{L})$, where $H$ is the mean curvature of $L$ and $F^{\perp}$ is the orthogonal projection of the position vector $F$ (that is, the inclusion $F:L\hookrightarrow{\mathbin{\mathbb{C}}}^{m}$) to the normal bundle $TL^{\perp}\subset T{\mathbin{\mathbb{C}}}^{m}|_{L}$, and $\alpha>0$ is constant.

This implies that (after reparametrizing by diffeomorphisms of $L$) the family of Lagrangians $L^{t}:=\sqrt{2\alpha t}\,L$ for $t\in(0,\infty)$ satisfy Lagrangian mean curvature flow. That is, Lagrangian MCF expands $L$ by dilations.

Similarly, we call $L$ an LMCF shrinker if $H=\alpha F^{\perp}$ for $\alpha<0$, and then $L^{t}:=\sqrt{2\alpha t}\,L$ for $t\in(-\infty,0)$ satisfy LMCF, so LMCF shrinks $L$ by dilations.

We call $L$ an LMCF translator if $H=v^{\perp}$, where $v\in{\mathbin{\mathbb{C}}}^{m}$ is the translating vector of $L$, and $v^{\perp}$ the orthogonal projection of $v$ to $TL^{\perp}$. Then $L^{t}:=L+tv$ for $t\in{\mathbin{\mathbb{R}}}$ satisfy LMCF, so Lagrangian MCF translates $L$ in ${\mathbin{\mathbb{C}}}^{m}$.