Liouville theorems for F-harmonic maps and their applications

TL;DR

This paper establishes Liouville theorems for F-harmonic maps under certain geometric and asymptotic conditions, with applications to minimal graphs and specific manifold classes.

Contribution

It introduces new Liouville theorems for F-harmonic maps considering Hessian and asymptotic conditions, extending previous results to broader manifold types.

Findings

Liouville theorems for F-harmonic maps under specified conditions

Applications to minimal graphs and pinched manifolds

Bernstein type result for entire minimal graphs

Abstract

We prove several Liouville theorems for F-harmonic maps from some complete Riemannian manifolds by assuming some conditions on the Hessian of the distance function, the degrees of F(t) and the asymptotic behavior of the map at infinity. In particular, the results can be applied to F-harmonic maps from some pinched manifolds, and can deduce a Bernstein type result for an entire minimal graph.