Invariant λ-translators for the Gauss curvature flow in Euclidean space

2025/08/24 by Aydin, Muhittin Evren, López, Rafael
#53A05 #53C21 #53C42 #Differential Geometry (math.DG) #FOS: Mathematics

paper · doi:10.48550/arxiv.2508.17321

Abstract

A λ-translator is a surface in Euclidean space ℝ³ whose Gauss curvature K satisfies K=⟨ N, v ⟩ +λ, where N is the Gauss map, v is a fixed direction, and λ∈ ℝ. In this paper, we classify all λ-translators that are invariant by a one-parameter group of translations and a one-parameter group of rotations.

Citations

• Rigidity of solitons of the Gauss curvature flow in Euclidean space
• Continuous family of surfaces translating by powers of Gauss curvature
• Flow by powers of the Gauss curvature in space forms
• Uniqueness of ancient solutions to Gauss curvature flow asymptotic to a cylinder
• Translating solutions to the Gauss curvature flow with flat sides

Related

• Translators of the Gauss curvature flow
• Invariant λ-translators in Lorentz-Minkowski space
• Invariant surfaces in Euclidean space with a log-linear density
• Rotational K^α-translators in Minkowski space
• Invariant translators of the Solvable group