Index one minimal surfaces in spherical space forms

TL;DR

This paper proves that orientable index one minimal surfaces in certain spherical space forms with large fundamental groups have genus at most two, confirming a conjecture for an infinite class of 3-manifolds.

Contribution

It establishes a genus bound for index one minimal surfaces in spherical space forms, confirming Schoen's conjecture in specific cases.

Findings

Orientable index one minimal surfaces have genus at most two in these manifolds.

Confirms Schoen's conjecture for an infinite class of 3-manifolds.

Provides new insights into the topology of minimal surfaces in spherical space forms.

Abstract

We prove that orientable index one minimal surfaces in spherical space forms with large fundamental group have genus at most two. This confirms a conjecture of R. Schoen for an infinite class of 3-manifolds.