Counting Minimal Tori In Riemannian Manifolds

TL;DR

This paper introduces a function that counts minimal tori in high-dimensional Riemannian manifolds and proves its invariance under metric perturbations, contributing to the understanding of minimal submanifolds.

Contribution

The paper defines a new counting function for minimal tori in Riemannian manifolds of dimension at least 6 and establishes its invariance under metric changes.

Findings

The count function is well-defined for minimal tori in high-dimensional manifolds.

The count function remains invariant under perturbations of the Riemannian metric.

Abstract

In this paper, we introduce a function which counts minimal tori in a Riemann manifold $(M, g)$ with $\mathrm{dim}\, M \ge 6$. Moreover, we show that this count function is invariant under perturbations of the metric.