Serena Dipierro, Jack Thompson, and Enrico Valdinoci
Some nonlocal formulas inspired by an identity of James Simons
(472K, pdf)

ABSTRACT.  Inspired by a classical identity proved by James Simons, we establish a new geometric formula in a nonlocal, possibly fractional, setting. 
Our formula also recovers the classical case in the limit, thus providing an approach to Simons' work that does not heavily rely on differential geometry.