2023/05/24 by Denis Polly, Polly, Denis
Biochemistry, Genetics and Molecular Biology · Mathematics · Physics and Astronomy · #53A10 (primary) #53A35 #53A40 33E05 (secondary) #53C52 #Advanced Differential Geometry Research #Dermatological and Skeletal Disorders #Differential Geometry (math.DG) #FOS: Mathematics #Geometric Analysis and Curvature Flows
paper · pdf · doi:10.48550/arxiv.2305.15514
openalex publication_date 2023/05/24 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28
We give a classification of rotational cmc surfaces in non-Euclidean space forms in terms of explicit parametrizations using Jacobi elliptic functions. Our method hinges on a Lie sphere geometric description of rotational linear Weingarten surfaces and can thus be applied to a more general class of surfaces. As another application of this framework, we give explicit parametrizations of a class of rotational constant harmonic mean curvature surfaces in hyperbolic space. In doing so, we close the last gaps in the classification of all channel linear Weingarten surfaces in space forms, started in Hertrich-Jeromin et all (2023).