A discrete analogue of the harmonic morphism and green kernel comparison theorems

By Hajime Urakawa. Glasgow Mathematical Journal, 2000

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Lifting harmonic morphisms I: metrized complexes and Berkovich skeleta (2013, unknown): “Harmonic morphisms of finite graphs were introduced by Urakawa in [45] and further explored in [8].”
Harmonic morphisms and hyperelliptic graphs (2007, methodology): “injective if and only if Gis (k+1)-edge-connected. 2. Harmonic morphisms 2.1. Deﬁnition and basic properties of harmonic morphisms. Harmonic morphisms between simple graphs were deﬁned and studied in [Ura00]. Here, we reproduce some deﬁnitions from [Ura00], but with several variations due to the fac”
Gonality of algebraic curves and graphs (2012, methodology): “ry of admissible coverings developed by J. Harris and D. Mumford in [HM82], and generalizes the combinatorial deﬁnition of harmonic morphisms given by M. Baker, S. Norine and H. Urakawa in [BN09] and [U00] for weightless graphs; this is why we use the word “harmonic”. Harmonic indexed morphisms have”