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arXiv · 2412.15612

$K^α$-translators of offset surfaces

Burcu Bektaş Demirci·Ferdağ Kahraman Aksoyak·Murat Babaarslan
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Abstract

In this paper, we study $K^α$--translators on parallel surfaces and canal surfaces in 3-dimensional Euclidean space $\mathbb{E}^3$. First, we investigate the condition under which two parallel surfaces can become $K^α$--translators moving with the same speed $w$. Then, we examine $K^α$--translators on canal surfaces and we show that if a canal surface is $K^α$--translator, then it must be a surface of revolution in $\mathbb{E}^3$. We also provide examples for moving a surface of revolution under $K$--flow (Gauss curvature flow) and $K^{-1/2}$--flow (inverse Gauss curvature flow) along a direction $w=(0,0,1)$ and we illustrate such surfaces using Wolfram Mathematica 10.4. Finally, we prove that no $K^α$--translators exist on the parallel surface of a rotational surface obtained from a canal surface with the same speed $w$, while the such rotational surfaces itself is a $K^α$--translator with speed $w$.

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Burcu Bektaş Demirci, Ferdağ Kahraman Aksoyak, Murat Babaarslan. 2024-12-20. $K^α$-translators of offset surfaces. https://arxiv.org/abs/2412.15612

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