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On the nonlocal curvatures of surfaces with or without boundary
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