On the nonlocal curvatures of surfaces with or without boundary

Brian Seguin, Paolo Podio-Guidugli, Roberto Paroni
2017 Communications on Pure and Applied Analysis  
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. 2000 Mathematics Subject Classification. Primary: 35R11, 49Q05; Secondary: 53A05.
doi:10.3934/cpaa.2018037 fatcat:phf6skivarcjxb5btcfhtliet4