A notion of nonlocal Gaussian curvature (Q281919)

Summary: A local notion of directional-curvature vector is proposed, which admits a nonlocal version that turns out to be the key ingredient to define both nonlocal mean curvature in the manner of [\textit{N. Abatangelo} and \textit{E. Valdinoci}, Numer. Funct. Anal. Optim. 35, No. 7--9, 793--815 (2014; Zbl 1296.53021)] and [\textit{X. Cabré} et al., ``Curves and surfaces with constant nonlocal mean curvature: meeting Alexandrov and Delaunay'', Preprint (2015), \url{arXiv:1503.00469}] and nonlocal Gaussian curvature, a new notion.