Extremal metrics on graphs I

Details Extremal metrics on graphs I Extremal metrics on graphs I

2000-01-28

arxiv.org/abs/math/0001169v1

Mathematics

Combinatorics

16 pages

Scientific paper

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

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