On the Nonlocal Curvatures of Surfaces with or without Boundary
Roberto Paroni, Paolo Podio–Guidugli, Brian Seguin · arXiv (Cornell University) · 2017
For surfaces without boundary, nonlocal notions of directional and mean curvatures have been recently given. Here, we develop alternative notions, special cases of which apply to surfaces with boundary. Our main tool is a new fractional or nonlocal area functional for compact surfaces.