The discrete Laplacian of a 2-simplicial complex

Yassin Chebbi

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arXiv · 1802.08422

The discrete Laplacian of a 2-simplicial complex

Yassin Chebbi

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Abstract

In this paper, we introduce the notion of oriented faces especially triangles in a connected oriented locally finite graph. This framework then permits to define the Laplace operator on this structure of the 2-simplicial complex. We develop the notion of $\chi$-completeness for the graphs, based on the cutoff functions. Moreover, we study essential self-adjointness of the discrete Laplacian from the $\chi$-completeness geometric hypothesis.

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Yassin Chebbi. 2018-02-23. The discrete Laplacian of a 2-simplicial complex. https://arxiv.org/abs/1802.08422

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