2023/12/22 by Paula Carretero, Carretero, Paula, Ildefonso Castro +1 · 2 citations
Mathematics · Physics and Astronomy · #53A04 #53A05 #Advanced Differential Geometry Research #Differential Geometry (math.DG) #FOS: Mathematics #Geometric Analysis and Curvature Flows #Mathematics and Applications
paper · pdf · doi:10.48550/arxiv.2312.14672
openalex publication_date 2023/12/22 · openalex created_date 2025/10/10 · openalex updated_date 2026/08/01
We solve the problem of prescribing different types of curvatures (principal, mean or Gaussian) on rotational surfaces in terms of arbitrary continuous functions depending on the distance from the surface to the axis of revolution. In this line, we get the complete explicit classification of the rotational surfaces with mean or Gauss curvature inversely proportional to the distance from the surface to the axis of revolution. We also provide new uniqueness results on some well known surfaces, such as the catenoid or the torus of revolution, and others less well known but equally interesting for their physical applications, such as the Mylar balloon or the Flamm's paraboloid.