Liouville type theorems for biharmonic maps

Abstract

<p>We prove Liouville type theorems for biharmonic maps from complete manifolds and from Euclidean balls.<br /> A variant of these Liouville-type problems is the study of the Dirichlet problem with constant boundary data, specifically, one aims to show that a harmonic map with constant boundary data is constant. In the case when the domain is a Euclidean ball.</p><p>We prove Liouville type theorems for biharmonic maps from complete manifolds and from Euclidean balls.<br /> A variant of these Liouville-type problems is the study of the Dirichlet problem with constant boundary data, specifically, one aims to show that a harmonic map with constant boundary data is constant. In the case when the domain is a Euclidean ball.</p>