An Aronsson type approach to extremal quasiconformal mappings

Details An Aronsson type approach to extremal quasiconformal mappings An Aronsson type approach to extremal quasiconformal mappings

2010-11-12

arxiv.org/abs/1011.2988v1

Mathematics

Analysis of PDEs

Scientific paper

We study $C^2$ extremal quasiconformal mappings in space and establish
necessary and sufficient conditions for a `localized' form of extremality in
the spirit of the work of G. Aronsson on absolutely minimizing Lipschitz
extensions. We also prove short time existence for smooth solutions of a
gradient flow of QC diffeomorphisms associated to the extremal problem.

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