A note on propagation of singularities of semiconcave functions of two variables

Abstract

P. Albano and P.

Cannarsa proved in 1999 that, under some applicable conditions, singularities of semiconcave functions in Euclidean n-dimensional space propagate along Lipschitz arcs. Further regularity properties of these arcs were proved by P.

Cannarsa and Y. Yu in 2009.

We prove that, for n=2, these arcs are very regular: they have finite turn.

Keywords

• semiconcave functions
• singularities