Energy-minimal diffeomorphisms between doubly connected Riemann surfaces

Details Energy-minimal diffeomorphisms between doubly connected Riemann surfaces Energy-minimal diffeomorphisms between doubly connected Riemann surfaces

2011-08-03

arxiv.org/abs/1108.0773v2

Mathematics

Complex Variables

32 pages. Some minor style changes appear in this version. arXiv admin note: text overlap with arXiv:1008.0652

Scientific paper

Let $N=(\Omega,\sigma)$ and $M=(\Omega^*,\rho)$ be doubly connected Riemann surfaces and assume that $\rho$ is a smooth metric with bounded Gauss curvature $\mathcal{K}$ and finite area. The paper establishes the existence of homeomorphisms between $\Omega$ and $\Omega^*$ that minimize the Dirichlet energy. In the class of all homeomorphisms $f \colon \Omega \onto \Omega^\ast$ between doubly connected domains such that $\Mod \Omega \le \Mod \Omega^\ast$ there exists, unique up to conformal authomorphisms of $\Omega$, an energy-minimal diffeomorphism which is a harmonic diffeomorphism. The results improve and extend some recent results of Iwaniec, Koh, Kovalev and Onninen (Inven. Math. (2011)), where the authors considered doubly connected domains in the complex plane w.r. to Euclidean metric.

Affiliated with

Also associated with

No associations

Rating

Energy-minimal diffeomorphisms between doubly connected Riemann surfaces 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 Energy-minimal diffeomorphisms between doubly connected Riemann surfaces, we encourage you to share that experience with our LandOfFree.com community. Your opinion is very important and Energy-minimal diffeomorphisms between doubly connected Riemann surfaces will most certainly appreciate the feedback.

Rate now

Comments { 0 }

Profile ID: LFWR-SCP-O-663674