Rotational surfaces with prescribed curvatures Carretero, Paula Castro, Ildefonso Rotational surfaces Principal curvatures Mean curvature 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. 2025-10-20T11:21:33Z 2025-10-20T11:21:33Z 2025-12 journal article Carretero, P., & Castro, I. (2025). Rotational surfaces with prescribed curvatures. Differential Geometry and Its Applications, 101(102298), 102298. https://doi.org/10.1016/j.difgeo.2025.102298 https://hdl.handle.net/10481/107173 10.1016/j.difgeo.2025.102298 eng http://creativecommons.org/licenses/by-nc/4.0/ open access Atribución-NoComercial 4.0 Internacional Elsevier