On conformal variational problems and free boundary continua
Artikel i vetenskaplig tidskrift, 2014

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.

free boundary continua

conformal embeddings

Hodge decomposition of vector fields and differential forms

calculus of variations

Författare

Stephen Marsland

Massey University

Robert I McLachlan

Massey University

Klas Modin

Göteborgs universitet

Chalmers, Matematiska vetenskaper, Matematik

Matthew Perlmutter

Universidade Federal de Minas Gerais

Journal of Physics A: Mathematical and Theoretical

1751-8113 (ISSN) 1751-8121 (eISSN)

Vol. 47 14 Art. no. 145204-

Fundament

Grundläggande vetenskaper

Ämneskategorier

Geometri

DOI

10.1088/1751-8113/47/14/145204