JournalsrmiVol. 28, No. 1pp. 127–140

Functions of class C1C^1 subject to a Legendre condition in an enhanced density set

  • Silvano Delladio

    Università di Trento, Povo, Italy
Functions of class $C^1$ subject to a Legendre condition in an enhanced density set cover

Abstract

We investigate certain second-order differential properties of functions and forms of class C1C^1 at the points around which a suitable Legendrian condition is “very densely verified”. In particular we provide a generalization of the classical identity d2=0d^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 C2C^2-rectifiability of the horizontal projection of a Legendrian rectifiable set is discussed.

Cite this article

Silvano Delladio, Functions of class C1C^1 subject to a Legendre condition in an enhanced density set. Rev. Mat. Iberoam. 28 (2012), no. 1, pp. 127–140

DOI 10.4171/RMI/670