Interior estimates for Translating solitons of the $Q_k$-flows in ${\mathbb{R}}^{n+1}$

Abstract

We prove interior gradient estimate and second order estimate for the $Q_k$-flow and $Q_k$-translators in ${\mathbb{R}}^{n+1}$. In addition, we show that $Q_k$-translator which are asymptotic to $o(|x|)$ cannot exist.