Liouville type theorems for biharmonic maps
Date
2010-08-02
Authors
Seddik Ouakkas
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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>
<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>