Uniqueness and non-existence of minimal submanifolds

TL;DR

This paper establishes uniqueness results for compact minimal submanifolds in various Riemannian manifolds, including Cartan-Hadamard spaces, with applications to geometric analysis.

Contribution

It provides new uniqueness theorems for minimal submanifolds in broad classes of Riemannian manifolds, extending previous results.

Findings

Uniqueness of compact minimal submanifolds in certain Riemannian manifolds

General results for minimal submanifolds in Cartan-Hadamard manifolds

Applications to problems in geometric analysis

Abstract

We provide uniqueness results for compact minimal submanifolds in a large class of Riemannian manifolds of arbitrary dimension. In the case compact and Cartan-Hadamard manifolds we obtain general results for these submanifolds. Several applications to Geometric Analysis are also showed.