The uniqueness of minimal maps into Cartan-Hadamard manifolds via the squared singular values

TL;DR

This paper proves a uniqueness theorem for minimal maps into non-positively curved Riemannian manifolds, extending previous results by analyzing convex functions related to squared singular values along geodesic homotopies.

Contribution

It improves a prior theorem on the uniqueness of minimal maps into Cartan-Hadamard manifolds by utilizing convexity properties of functions based on squared singular values.

Findings

Established a new uniqueness theorem for minimal maps

Extended previous results to more general Riemannian manifolds

Used convexity of functions along geodesic homotopies

Abstract

In this paper, we give a uniqueness theorem for the Dirichlet problem of minimal maps into general Riemannian manifolds with non-positive sectional curvature, improving Theorem 5.2 of Lee-Ooi-Tsui's paper published in J. Geom. Anal.. The proof of this theorem is based on the convexity of several functions in terms of squared singular values along the geodesic homotopy of two given minimal maps.