Revista Matemática Iberoamericana


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Volume 28, Issue 1, 2012, pp. 127–140
DOI: 10.4171/RMI/670

Published online: 2012-01-20

Functions of class $C^1$ subject to a Legendre condition in an enhanced density set

Silvano Delladio[1]

(1) Università di Trento, Povo, Italy

We investigate certain second-order differential properties of functions and forms of class $C^1$ at the points around which a suitable Legendrian condition is “very densely verified”. In particular we provide a generalization of the classical identity $d^2=0$ on differential forms and some results about second-order osculating properties of graphs. Particular emphasis is placed on the case when the condition is verified in a locally finite perimeter set. A conjecture about the $C^2$-rectifiability of the horizontal projection of a Legendrian rectifiable set is discussed.

Keywords: Enhanced density, parabolic blow-up, $C^2$-rectifiable sets

Delladio Silvano: Functions of class $C^1$ subject to a Legendre condition in an enhanced density set. Rev. Mat. Iberoamericana 28 (2012), 127-140. doi: 10.4171/RMI/670