Embedded loops in the hyperbolic plane with prescribed, almost constant curvature

2018/03/02 by Roberta Musina, Musina, Roberta, Fabio Zuddas +1
Mathematics · #Analytic and geometric function theory #Differential Geometry (math.DG) #FOS: Mathematics #Geometric Analysis and Curvature Flows #Mathematics and Applications #math.DG

paper · pdf · doi:10.48550/arxiv.1803.00856

Theorems numbering has been changed; few misprints were fixed

openalex publication_date 2018/03/02 · arxiv created 2018/03/19 · arxiv updated 2018/03/20 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

Abstract

Given a constant k>1 and a real valued function K on the hyperbolic plane \mathbb H², we study the problem of finding, for any ε≈ 0, a closed and embedded curve u^ε in \mathbb H² having geodesic curvature k+εK(u^ε) at each point.

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