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An Aronsson Type Approach To Extremal Quasiconformal Mappings, Luca Capogna, Andrew Raich
An Aronsson Type Approach To Extremal Quasiconformal Mappings, Luca Capogna, Andrew Raich
Mathematics Sciences: Faculty Publications
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.