English

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