Extremal metrics on graphs I
Combinatorics
2007-05-23 v1
Abstract
We define a number of natural (from geometric and combinatorial points of view) deformation spaces of valuations on finite graphs, and study functions over these deformation spaces. These functions include both direct metric invariants (girth, diameter), and spectral invariants (the determinant of the Laplace operator, or complexity; bottom non-zero eigenvalue of the Laplace operator). We show that almost all of these functions are, surprisingly, convex, and we characterize the valuations extremizing these invariant
Cite
@article{arxiv.math/0001169,
title = {Extremal metrics on graphs I},
author = {Dmitry Jakobson and Igor Rivin},
journal= {arXiv preprint arXiv:math/0001169},
year = {2007}
}
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16 pages