On conformal variational problems and free boundary continua

• 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.

Subject headings

NATURVETENSKAP  -- Matematik -- Geometri (hsv//swe)

NATURAL SCIENCES  -- Mathematics -- Geometry (hsv//eng)

Keyword

free boundary continua

conformal embeddings

Hodge decomposition of vector fields and differential forms

calculus of variations

calculus of variations; conformal embeddings; free boundary continua; Hodge decomposition of vector fields and differential forms

Publication and Content Type

art (subject category)

ref (subject category)