Examples of stable embedded minimal spheres without area bounds

TL;DR

This paper demonstrates that on any 3-manifold, there are metrics allowing for families of stable minimal 2-spheres with unbounded area, extending previous results to broader contexts.

Contribution

It generalizes prior work by proving the existence of metrics with unbounded stable minimal spheres on any 3-manifold.

Findings

Existence of metrics with unbounded stable minimal 2-spheres

Extension of previous results to all 3-manifolds

Open set of such metrics in the space of all metrics

Abstract

The author proves that there is an open non empty set of metrics on any 3-manifold such that there exists a family of stably embedded minimal 2-spheres whose area is unbounded. This generalizes the work of T. Colding and W. Minicozzi who have shown an analogous result for the torus and B. Dean who showed the positive genus case.