Nonplanar minimal spheres in ellipsoids of revolution
Differential Geometry
2025-11-05 v4
Abstract
We use global bifurcation techniques to establish the existence of arbitrarily many geometrically distinct nonplanar embedded smooth minimal 2-spheres in sufficiently elongated 3-dimensional ellipsoids of revolution. More precisely, we quantify the growth rate of the number of such minimal spheres, and describe their asymptotic behavior as the ellipsoids converge to a cylinder.
Keywords
Cite
@article{arxiv.2111.14995,
title = {Nonplanar minimal spheres in ellipsoids of revolution},
author = {Renato G. Bettiol and Paolo Piccione},
journal= {arXiv preprint arXiv:2111.14995},
year = {2025}
}
Comments
LaTeX2e, 32 pages, 4 figures, final (revised) version. To appear in Ann. Sc. Norm. Super. Pisa Cl. Sci