On the similarity between the Iwasawa projection and the diagonal part
J. J. Duistermaat (1984)
Mémoires de la Société Mathématique de France
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On the similarity between the Iwasawa projection and the diagonal part
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Let be a -step Carnot group. The first aim of this paper is to show an interplay between volume and -perimeter, using one-dimensional horizontal slicing. What we prove is a kind of Fubini theorem for -regular submanifolds of codimension one. We then give some applications of this result: slicing of functions, integral geometric formulae for volume and -perimeter and, making use of a suitable notion of convexity, called, we state a Cauchy type formula for -convex sets. Finally,...