K^α-translators of offset surfaces

2024/12/20 by Burcu Bektaş Demirci, Demirci, Burcu Bektaş, Ferdağ Kahraman Aksoyak +3
Computer Science · Engineering · #53A05 #Advanced Numerical Analysis Techniques #Computational Geometry and Mesh Generation #Differential Geometry (math.DG) #Digital Image Processing Techniques #FOS: Mathematics

paper · pdf · doi:10.48550/arxiv.2412.15612

openalex publication_date 2024/12/20 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

Abstract

In this paper, we study K^α--translators on parallel surfaces and canal surfaces in 3-dimensional Euclidean space 𝔼³. 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 𝔼³. 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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