On the Nonlocal Curvatures of Surfaces with or without Boundary

Roberto Paroni; Paolo Podio-Guidugli; Brian Seguin

On the Nonlocal Curvatures of Surfaces with or without Boundary

Differential Geometry 2017-07-20 v3

Authors: Roberto Paroni , Paolo Podio-Guidugli , Brian Seguin

Abstract

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.

Keywords

nonlocal curvature surfaces with boundary fractional area functional directional curvature mean curvature compact surfaces

Cite

@article{arxiv.1701.06513,
  title  = {On the Nonlocal Curvatures of Surfaces with or without Boundary},
  author = {Roberto Paroni and Paolo Podio-Guidugli and Brian Seguin},
  journal= {arXiv preprint arXiv:1701.06513},
  year   = {2017}
}