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Sobolev mappings, co-area formula and related topics. (English) Zbl 0988.28002
Vodop’yanov, S. K. (ed.), Proceedings on analysis and geometry. International conference in honor of the 70th birthday of Professor Yu. G. Reshetnyak, Novosibirsk, Russia, August 30-September 3, 1999. Novosibirsk: Izdatel’stvo Instituta Matematiki Im. S. L. Soboleva SO RAN. 227-254 (2000).
The author generalizes the classical area and co-area formulas to the setting of Sobolev mappings, in particular, one of the versions of the co-area formula proposed involves the integral-geometric measure. The proof is based on a Sard-type theorem for Borel mappings between Euclidean spaces which may be of independent interest. The results obtained are applied to the minimization problem for harmonic mappings.
For the entire collection see [Zbl 0971.00061].

MSC:
28A75 Length, area, volume, other geometric measure theory
58C35 Integration on manifolds; measures on manifolds
46E35 Sobolev spaces and other spaces of “smooth” functions, embedding theorems, trace theorems
58D15 Manifolds of mappings
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