A divergence-like characterization of admissible functions on digraphs
type: Item
instance of: scholarly article
title: A divergence-like characterization of admissible functions on digraphs
zbMATH Open document ID: 1062.53019
author: Gen-ichi Oshikiri
published in: Tôhoku Mathematical Journal. Second Series
publication date: 2004-11-05T00:00:00Z
review text: A smooth function on a manifold with a codimension-one-foliation is called admissible if there is a Riemannian metric such that the function is the mean curvature function of the leaves. In a previous paper [Tohoku Math. J., II. Ser. 51, No. 2, 227--236 (1999; Zbl 0934.57034)] the author has established a \(1-1\)-correspondence between codimension-one-foliations of manifolds and directed graphs. The main theorem of the present paper gives a similar correspondence between smooth admissible functions and certain labelings (defined in terms of a coboundary operator) of the associated digraph. In some sense the labeling on the combinatorial side corresponds to taking the divergence of the unit normal vector of the foliation.
Mathematics Subject Classification ID: 53C12
Mathematics Subject Classification ID: 05C20
Mathematics Subject Classification ID: 57R30
zbMATH DE Number: 2114239
zbMATH Keywords: mean curvature
zbMATH Keywords: Cheeger constant
reviewed by: Wolfgang Kühnel
MaRDI profile type: Publication
full work available at URL: https://doi.org/10.2748/tmj/1113246547
OpenAlex ID: W2035782849
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DOI: 10.2748/TMJ/1113246547
description: scientific article; zbMATH DE number 2114239