Erratum to: "Ahlfors Q -regular spaces with arbitrary Q &gt; 1 admitting weak Poincar� inequality", in GAFA 10 (2000)

Laakso, Tomi

doi:10.1007/s00039-002-8261-9

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Sobolev Mappings between Manifolds and Metric Spaces

Hajłasz

Sobolev Spaces in Mathematics I

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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 CarnotCarathéodory 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.

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