Curvature on a graph via its geometric spectrum
Paul Baird[1]
- [1] Laboratoire de Mathématiques de Bretagne Atlantique Université de Bretagne Occidentale 6 av. Victor Le Gorgeu – CS 93837 29238 BREST CEDEX FRANCE
Actes des rencontres du CIRM (2013)
- Volume: 3, Issue: 1, page 97-105
- ISSN: 2105-0597
Access Full Article
top
Abstract
topHow to cite
topBaird, Paul. "Curvature on a graph via its geometric spectrum." Actes des rencontres du CIRM 3.1 (2013): 97-105. <http://eudml.org/doc/275380>.
@article{Baird2013,
abstract = {We approach the problem of defining curvature on a graph by attempting to attach a ‘best-fit polytope’ to each vertex, or more precisely what we refer to as a configured star. How this should be done depends upon the global structure of the graph which is reflected in its geometric spectrum. Mean curvature is the most natural curvature that arises in this context and corresponds to local liftings of the graph into a suitable Euclidean space. We discuss some examples.},
affiliation = {Laboratoire de Mathématiques de Bretagne Atlantique Université de Bretagne Occidentale 6 av. Victor Le Gorgeu – CS 93837 29238 BREST CEDEX FRANCE},
author = {Baird, Paul},
journal = {Actes des rencontres du CIRM},
keywords = {graph theory; curvature; geometric spectrum; shape recognition},
language = {eng},
month = {11},
number = {1},
pages = {97-105},
publisher = {CIRM},
title = {Curvature on a graph via its geometric spectrum},
url = {http://eudml.org/doc/275380},
volume = {3},
year = {2013},
}
TY - JOUR
AU - Baird, Paul
TI - Curvature on a graph via its geometric spectrum
JO - Actes des rencontres du CIRM
DA - 2013/11//
PB - CIRM
VL - 3
IS - 1
SP - 97
EP - 105
AB - We approach the problem of defining curvature on a graph by attempting to attach a ‘best-fit polytope’ to each vertex, or more precisely what we refer to as a configured star. How this should be done depends upon the global structure of the graph which is reflected in its geometric spectrum. Mean curvature is the most natural curvature that arises in this context and corresponds to local liftings of the graph into a suitable Euclidean space. We discuss some examples.
LA - eng
KW - graph theory; curvature; geometric spectrum; shape recognition
UR - http://eudml.org/doc/275380
ER -
References
top- P. Baird, A class of quadratic difference equations on a finite graph, arXiv:1109.3286 [math-ph]
- P. Baird, Constant mean curvature polytopes and hypersurfaces via projections, Differential Geom. and its Applications online version nov. 2013 Zbl1284.52015MR3159958
- P. Baird, Emergence of geometry in a combinatorial universe, J. Geom. and Phys. 74 ((2013)), 185-195 Zbl1278.05079MR3118581
- P. Baird, Information, universality and consciousness: a relational perspective, Mind and Matter 11(2) ((2013)), 21-43
- P. Baird, An invariance property for frameworks in Euclidean space, Linear Algebra and its Applications 440 ((2014)), 243-265 Zbl1292.05166MR3134268
- P. Baird, M. Wehbe, Twistor theory on a finite graph, Comm. Math. Phys. 304(2) ((2011)), 499-511 Zbl1216.81090MR2795330
- S. Barré, Real and discrete holomorphy: introduction to an algebraic approach, J. Math. Pures Appl. 87 ((2007)), 495-513 Zbl1146.31007MR2322148
- C. Delaunay, Sur la surface de révolution dont la courbure moyenne est constante, 6 ((1841)), 309-320
- R. Descartes, Progymnasmata de solidorum elementis, Oeuvres de Descartes X, 265-276
- M. G. Eastwood, R. Penrose, Drawing with complex numbers, Math. Intelligencer 22 ((2000)), 8-13 Zbl1052.51505MR1796760
NotesEmbed ?
topYou must be logged in to post comments.
To embed these notes on your page include the following JavaScript code on your page where you want the notes to appear.