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arXiv · 1404.5690

Conformally Covariant Operators and Conformal Invariants on Weighted Graphs

Dmitry Jakobson·Thomas Ng·Matthew Stevenson·Mashbat Suzuki
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Abstract

Let G be a finite connected simple graph. We define the moduli space of conformal structures on G. We propose a definition of conformally covariant operators on graphs, motivated by [25]. We provide examples of conformally covariant operators, which include the edge Laplacian and the adjacency matrix on graphs. In the case where such an operator has a nontrivial kernel, we construct conformal invariants, providing discrete counterparts of several results in [11,12] established for Riemannian manifolds. In particular, we show that the nodal sets and nodal domains of null eigenvectors are conformal invariants.

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Dmitry Jakobson, Thomas Ng, Matthew Stevenson, Mashbat Suzuki. 2014-10-05. Conformally Covariant Operators and Conformal Invariants on Weighted Graphs. https://arxiv.org/abs/1404.5690

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