Functions of class $C^1$ subject to a Legendre condition in an enhanced density set
Silvano Delladio · Revista Matemática Iberoamericana · 2012
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.