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- W4320341780 abstract "Cheeger-type inequalities in which the decomposability of a graph and the spectral gap of its Laplacian mutually control each other play an important role in graph theory and network analysis, in particular in the context of expander theory. The natural problem, however, to extend such inequalities to simplicial complexes and their higher order Eckmann Laplacians has been open for a long time. The question is not only to prove an inequality, but also to identify the right Cheeger-type constant in the first place. Here, we solve this problem. Our solution involves and combines constructions from simplicial topology, signed graphs, Gromov filling radii and an interpolation between the standard 2-Laplacians and the analytically more difficult 1-Laplacians, for which, however, the inequalities become equalities. It is then natural to develop a general theory for $p$-Laplacians on simplicial complexes and investigate the related Cheeger-type inequalities." @default.
- W4320341780 created "2023-02-13" @default.
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- W4320341780 date "2023-02-02" @default.
- W4320341780 modified "2023-09-27" @default.
- W4320341780 title "Cheeger inequalities on simplicial complexes" @default.
- W4320341780 doi "https://doi.org/10.48550/arxiv.2302.01069" @default.
- W4320341780 hasPublicationYear "2023" @default.
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