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Bulletin of the American Mathematical Society

ISSN 1088-9485(online) ISSN 0273-0979(print)



Nonsmooth calculus

Author: Juha Heinonen
Journal: Bull. Amer. Math. Soc. 44 (2007), 163-232
MSC (2000): Primary 28A75, 49J52, 53C23, 51-02
Published electronically: January 24, 2007
MathSciNet review: 2291675
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Abstract: We survey recent advances in analysis and geometry, where first order differential analysis has been extended beyond its classical smooth settings. Such studies have applications to geometric rigidity questions, but are also of intrinsic interest. The transition from smooth spaces to singular spaces where calculus is possible parallels the classical development from smooth functions to functions with weak or generalized derivatives. Moreover, there is a new way of looking at the classical geometric theory of Sobolev functions that is useful in more general contexts.

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Additional Information

Juha Heinonen
Affiliation: Department of Mathematics, University of Michigan, Ann Arbor, Michigan 48109

Received by editor(s): November 7, 2005
Received by editor(s) in revised form: June 16, 2006
Published electronically: January 24, 2007
Additional Notes: This paper constitutes an expanded version of the AMS invited address given by the author in Boulder, Colorado, in October 2003
The author is grateful for the support and hospitality of MSRI and UC Berkeley, where the bulk of this paper was prepared during a visit in 2002-2003. Supported also by NSF grants DMS 0353549 and DMS 0244421.
Article copyright: © Copyright 2007 American Mathematical Society
The copyright for this article reverts to public domain 28 years after publication.