Existence of energy-minimal diffeomorphisms between doubly connected domains

Details Existence of energy-minimal diffeomorphisms between doubly connected domains Existence of energy-minimal diffeomorphisms between doubly connected domains

2010-08-03

arxiv.org/abs/1008.0652v1

Invent. Math. 186 (2011), no. 3, 667-707

Mathematics

Complex Variables

34 pages, no figures

Scientific paper

10.1007/s00222-011-0327-6

The paper establishes the existence of homeomorphisms between two planar domains that minimize the Dirichlet energy. Specifically, among all homeomorphisms f : R -> R* between bounded doubly connected domains such that Mod (R) < Mod (R*) there exists, unique up to conformal authomorphisms of R, an energy-minimal diffeomorphism. No boundary conditions are imposed on f. Although any energy-minimal diffeomorphism is harmonic, our results underline the major difference between the existence of harmonic diffeomorphisms and the existence of the energy-minimal diffeomorphisms. The existence of globally invertible energy-minimal mappings is of primary pursuit in the mathematical models of nonlinear elasticity and is also of interest in computer graphics.

Affiliated with

Also associated with

No associations

Rating

Existence of energy-minimal diffeomorphisms between doubly connected domains does not yet have a rating. At this time, there are no reviews or comments for this scientific paper.

If you have personal experience with Existence of energy-minimal diffeomorphisms between doubly connected domains, we encourage you to share that experience with our LandOfFree.com community. Your opinion is very important and Existence of energy-minimal diffeomorphisms between doubly connected domains will most certainly appreciate the feedback.

Rate now

Comments { 0 }

Profile ID: LFWR-SCP-O-81898