An example of rotationally symmetric $Q_{n-1}$-translators and a non-existence theorem in $\mathbb{R}^{n+1}$

TL;DR

This paper proves a non-existence theorem for entire $Q_{n-1}$-translators in $ eal^{n+1}$, provides an example of a non-entire complete translator, and introduces a Tangential Principle for $Q_k$-translators, advancing understanding of geometric flows.

Contribution

It establishes a non-existence result for entire $Q_{n-1}$-translators and introduces a Tangential Principle, offering new insights into $Q_k$-translators in Euclidean space.

Findings

Proved a non-existence theorem for entire $Q_{n-1}$-translators.

Constructed an example of a non-entire complete $Q_{n-1}$-translator.

Formulated a Tangential Principle for $Q_k$-translators.

Abstract

The main result in this paper is a non-existence Theorem of entire $Q_{n-1}$-translators in $\mathbb{R}^{n+1}$. In addition, an example of non-entire complete $Q_{n-1}$-translator has been found and a Tangential Principle for $Q_k$-translators in $\mathbb{R}^{n+1}$.