Scholarlink

<p>In this paper, we consider λ-translating solitons in ℝ<sup>3</sup>. These surfaces are critical points of the weighted area when the density is a coordinate function. If λ = 0, these surfaces evolve by translations along the mean curvature flow. We give a full classification of λ-translating solitons that satisfy a linear Weingarten relation between their curvatures. These surfaces are planes, circular cylinders, grim reapers and certain types of cylindrical surfaces. We also prove that planes and circular cylinders are the only λ-translating soliton with constant squared norm of the second fundamental form.</p>

错误：搜索内容不能为空，请输入英文关键词
错误：关键词超出字数限制，请精简
高级检索

Translating Solitons in ℝ3 of Linear Weingarten Type

  • 期刊论文

  • 发表日期：

    2025年6月15日

查看全文
  • Yu Fu,
  • Rafael López,
  • Yanru Luo,
  • Dan Yang

摘要

In this paper, we consider λ-translating solitons in ℝ3. These surfaces are critical points of the weighted area when the density is a coordinate function. If λ = 0, these surfaces evolve by translations along the mean curvature flow. We give a full classification of λ-translating solitons that satisfy a linear Weingarten relation between their curvatures. These surfaces are planes, circular cylinders, grim reapers and certain types of cylindrical surfaces. We also prove that planes and circular cylinders are the only λ-translating soliton with constant squared norm of the second fundamental form.