We investigate certain second-order differential properties of functions and forms of class at the points around which a suitable Legendrian condition is “very densely verified”. In particular we provide a generalization of the classical identity 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 -rectifiability of the horizontal projection of a Legendrian rectifiable set is discussed.
Cite this article
Silvano Delladio, Functions of class subject to a Legendre condition in an enhanced density set. Rev. Mat. Iberoam. 28 (2012), no. 1, pp. 127–140DOI 10.4171/RMI/670