Surfaces and Hypersurfaces with Prescribed Radial Mean Curvature
Differential Geometry
2025-10-14 v1 Geometric Topology
Abstract
In this work, we provide a local classification of certain special classes of surfaces determined by the prescription of the radial mean curvature in terms of the height and angle functions. Moreover, we introduce a special class of hypersurfaces, and we also provide a local classification of these three-dimensional hypersurfaces whose second mean curvature vanishes. Finally, we present a recursive method for constructing such hypersurfaces, extending the same curvature prescription approach to higher dimensions.
Keywords
Cite
@article{arxiv.2510.11669,
title = {Surfaces and Hypersurfaces with Prescribed Radial Mean Curvature},
author = {Marcelo Lopes Ferro and Armando M. V. Corro},
journal= {arXiv preprint arXiv:2510.11669},
year = {2025}
}