Communications in Analysis and Geometry

Volume 22 (2014)

Number 3

A construction of biharmonic maps into homogeneous spaces

Pages: 451 – 468

DOI: http://dx.doi.org/10.4310/CAG.2014.v22.n3.a3

Author

Roger Moser (Department of Mathematical Sciences, University of Bath, United Kingdom)

Abstract

Biharmonic maps are the solutions of a variational problem, but they are difficult to study with variational methods, in part due to the lack of coercivity of the underlying functional. Recently Hornung was able to apply the direct method to a modified functional under the assumption that the dimension of the domain is 3 or 4. In this paper, the corresponding minimizers are studied in the case of a homogeneous target space. It is shown that they also represent minimizers of the original functional among a suitable class of comparison maps. Moreover, they solve the corresponding Euler-Lagrange equation if it is interpreted in a sufficiently weak sense.

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