Sobolev Mappings between Manifolds and Metric Spaces

  • Piotr Hajlasz
Part of the International Mathematical Series book series (IMAT, volume 8)

In connection with the theory of p-harmonic mappings, Eells and Lemaire raised a question about density of smooth mappings in the space of Sobolev mappings between manifolds. Recently Hang and Lin provided a complete solution to this problem. The theory of Sobolev mappings between manifolds has been extended to the case of Sobolev mappings with values into metric spaces. Finally analysis on metric spaces, the theory of Carnot-Carathéodory spaces, and the theory of quasiconformal mappings between metric spaces led to the theory of Sobolev mappings between metric spaces. The purpose of this paper is to provide a self-contained introduction to the theory of Sobolev spaces between manifolds and metric spaces. The paper also discusses new results of the author.


Banach Space Sobolev Space Lipschitz Mapping Heisenberg Group Quasiconformal Mapping 
These keywords were added by machine and not by the authors. This process is experimental and the keywords may be updated as the learning algorithm improves.


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© Springer Science+Business Media, LLC 2009

Authors and Affiliations

  • Piotr Hajlasz
    • 1
  1. 1.University of PittsburghPittsburghUSA

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