Existence of two embedded minimal spheres in $S^3$ with an arbitrary metric

Zhichao Wang; Xin Zhou

Existence of two embedded minimal spheres in $S^3$ with an arbitrary metric

Differential Geometry 2026-07-09 v1 Analysis of PDEs Geometric Topology

Authors: Zhichao Wang , Xin Zhou

Abstract

We prove that $S^3$ endowed with an arbitrary Riemannian metric $g$ admits at least two embedded minimal spheres. The proof is based on an iterative scheme of relative min-max constructions.

Keywords

embedded minimal sphere Riemannian metric min-max construction three-sphere

Cite

@article{arxiv.2607.08631,
  title  = {Existence of two embedded minimal spheres in $S^3$ with an arbitrary metric},
  author = {Zhichao Wang and Xin Zhou},
  journal= {arXiv preprint arXiv:2607.08631},
  year   = {2026}
}

Comments

32 pages, 1 figure; comments are welcome