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On conformal variational problems and free boundary continua

Journal article
Authors Stephen Marsland
Robert I McLachlan
Klas Modin
Matthew Perlmutter
Published in Journal of Physics A: Mathematical and Theoretical
Volume 47
Issue 14
Pages Art. no. 145204
ISSN 1751-8113
Publication year 2014
Published at Department of Mathematical Sciences, Mathematics
Pages Art. no. 145204
Language en
Keywords calculus of variations; conformal embeddings; free boundary continua; Hodge decomposition of vector fields and differential forms
Subject categories Geometry


We develop a framework for deriving governing partial differential equations for variational problems on spaces of conformal mappings. The main motivation is to obtain differential equations for the conformal motion of free boundary continua, of interest in image and shape registration. A fundamental tool in the paper, the Hodge–Morrey–Friedrichs decompositions of differential forms on manifolds with boundaries, is used to identify the orthogonal complement of the subspace of conformal mappings. A detailed presentation of these decompositions is included in the paper.

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