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ЖУРНАЛЫ // Eurasian Mathematical Journal // Архив

Eurasian Math. J., 2013, том 4, номер 2, страницы 10–48 (Mi emj121)

Эта публикация цитируется в 36 статьях

Approximate differentiability of mappings of Carnot–Carathéodory spaces

S. G. Basalaeva, S. K. Vodopyanovb

a Novosibirsk State University
b Sobolev Institute of Mathematics of the Siberian Branch of the Russian Academy of Sciences

Аннотация: We study the approximate differentiability of measurable mappings of Carnot–Carathéodory spaces. We show that the approximate differentiability almost everywhere is equivalent to the approximate differentiability along the basic horizontal vector fields almost everywhere. As a geometric tool we prove the generalization of Rashevsky–Chow theorem for $C^1$-smooth vector fields. The main result of the paper extends theorems on approximate differentiability proved by Stepanoff (1923, 1925) and Whitney (1951) for Euclidean spaces and by Vodopyanov (2000) for Carnot groups.

Ключевые слова и фразы: approximate differentiability, Carnot–Carathéodory space.

MSC: 53C17, 58C25, 28A75

Поступила в редакцию: 27.09.2010

Язык публикации: английский



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