Closed minimal surfaces of high Morse index in manifolds of negative curvature

TL;DR

This paper proves that in negatively curved three-manifolds, there exist closed minimal surfaces with arbitrarily high Morse index, expanding understanding of minimal surface complexity in such geometries.

Contribution

It establishes the existence of high Morse index minimal surfaces in negatively curved three-manifolds, a new result in geometric analysis.

Findings

Existence of closed minimal surfaces with arbitrarily high Morse index

Extension of minimal surface theory to negatively curved three-manifolds

Advancement in understanding the topology of minimal surfaces in curved spaces

Abstract

We show that compact Riemannian three-manifolds with negative sectional curvature possess closed minimal surfaces of arbitrarily high Morse index.