Liouville theorems for $f$-harmonic maps into Hadamard spaces

TL;DR

This paper establishes Liouville theorems for finite energy harmonic maps from weighted manifolds into Hadamard spaces, extending classical results to a broader geometric context.

Contribution

It introduces Liouville theorems for $f$-harmonic maps into Hadamard spaces, generalizing previous harmonic map results to weighted manifolds.

Findings

Liouville theorems hold for harmonic maps with finite energy

Extension of classical harmonic map results to weighted manifolds

Application to $f$-harmonic maps into Hadamard spaces

Abstract

In this paper, we study harmonic functions on weighted manifolds and harmonic maps from weighted manifolds into Hadamard spaces introduced by Korevaar and Schoen. We prove Liouville theorems for these harmonic maps with finite energy.