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A General Approach to Equivariant Biharmonic Maps

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A Correction to this article was published on 01 November 2018

Abstract

In this paper we describe a 1-dimensional variational approach to the analytical construction of equivariant biharmonic maps. Our goal is to provide a direct method which enables analysts to compute directly the analytical conditions which guarantee biharmonicity in the presence of suitable symmetries. In the second part of our work, we illustrate and discuss some examples. In particular, we obtain a 1-dimensional stability result, and also show that biharmonic maps do not satisfy the classical maximum principle proved by Sampson for harmonic maps.

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Authors and Affiliations

  1. Università degli Studi di Cagliari, Dipartimento di Matematica e Informatica, Via Ospedale 72, 09124, Cagliari, Italia

    Stefano Montaldo

  2. Università degli Studi di Cagliari, Dipartimento di Matematica e Informatica, Viale Merello 93, 09123, Cagliari, Italia

    Andrea Ratto

Authors
  1. Stefano Montaldo
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  2. Andrea Ratto
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Correspondence to Stefano Montaldo.

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Work supported by Contributo d’Ateneo, University of Cagliari, Italy.

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Montaldo, S., Ratto, A. A General Approach to Equivariant Biharmonic Maps. Mediterr. J. Math. 10, 1127–1139 (2013). https://doi.org/10.1007/s00009-012-0207-3

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  • DOI: https://doi.org/10.1007/s00009-012-0207-3

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