Minimal Submanifolds via Complex-Valued Eigenfunctions

TL;DR

This paper introduces a novel method for constructing minimal submanifolds in Riemannian geometry using complex-valued eigenfunctions, especially effective in compact ambient manifolds.

Contribution

The paper presents a new technique leveraging complex-valued eigenfunctions to generate minimal submanifolds, expanding the toolkit in Riemannian geometry.

Findings

Method successfully constructs minimal submanifolds in compact manifolds.

Provides a new approach linking eigenfunctions to geometric minimality.

Enhances understanding of the relationship between spectral properties and minimal surfaces.

Abstract

In this work we introduce a new method for manufacturing minimal submanifolds in Riemannian geometry. For this we employ the so called complex-valued eigenfunctions. This is particularly interesting in the cases when the Riemannian ambient manifold is compact.