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Mathematics > Analysis of PDEs

arXiv:1804.04100 (math)
[Submitted on 11 Apr 2018 (v1), last revised 20 Sep 2018 (this version, v2)]

Title:Constant Nonlocal Mean Curvatures surfaces and related problems

Authors:Mouhamed Moustapha Fall
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Abstract:The notion of Nonlocal Mean Curvature (NMC) appears recently in the mathematics literature. It is an extrinsic geometric quantity that is invariant under global reparameterization of a surface and provide a natural extension of the classical mean curvature. We describe some properties of the NMC and the quasilinear differential operators that are involved when it acts on graphs. We also survey recent results on surfaces having constant NMC and describe their intimate link with some problems arising in the study of overdetermined boundary value problems.
Comments: Proc. Int. Cong. of Math. 2018 Rio de Janeiro, Vol. 1 (21-30)
Subjects: Analysis of PDEs (math.AP); Differential Geometry (math.DG)
Cite as: arXiv:1804.04100 [math.AP]
  (or arXiv:1804.04100v2 [math.AP] for this version)
  https://doi.org/10.48550/arXiv.1804.04100
Related DOI: https://doi.org/10.9999/icm2018-v1-p21

Submission history

From: Mouhamed Moustapha Fall [view email]
[v1] Wed, 11 Apr 2018 17:11:05 UTC (28 KB)
[v2] Thu, 20 Sep 2018 07:46:02 UTC (28 KB)
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