Closed p-Elastic Curves in Spheres of \mathbbL³

2024/04/12 by Álvaro Pámpano, Pampano, Alvaro, Miraj Samarakkody +3
Computer Science · Mathematics · #Advanced Mathematical Modeling in Engineering #Analytic and geometric function theory #Differential Geometry (math.DG) #FOS: Mathematics #Geometric Analysis and Curvature Flows

paper · pdf · doi:10.48550/arxiv.2404.08593

openalex publication_date 2024/04/12 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

Abstract

For every p∈ℝ, we study p-elastic curves in the hyperbolic plane ℍ² and in the de Sitter 2-space ℍ₁². We analyze the existence of closed p-elastic curves with nonconstant curvature showing that in the hyperbolic plane ℍ² these curves exist provided that p>1, while in the de Sitter 2-space ℍ₁² the restriction p<0 must be satisfied.

Related

• Instability of Closed p-Elastic Curves in \mathbbS²
• The elastic flow of curves in the hyperbolic plane
• Regularity and structure of non-planar p-elasticae
• Extension of a problem of Euler in ℍ² and in \mathbbS²
• Constrained elastic curves and surfaces with spherical curvature lines