@misc{10481/107173,
year = {2025},
month = {12},
url = {https://hdl.handle.net/10481/107173},
abstract = {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.},
publisher = {Elsevier},
keywords = {Rotational surfaces},
keywords = {Principal curvatures},
keywords = {Mean curvature},
title = {Rotational surfaces with prescribed curvatures},
doi = {10.1016/j.difgeo.2025.102298},
author = {Carretero, Paula and Castro, Ildefonso},
}