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math.AP2016
Minimisers of the Allen-Cahn equation on hyperbolic graphs
Blaz Mramor
We investigate minimal solutions of the Allen-Cahn equation on a Gromov-hyperbolic graph. Under some natural conditions on the graph, we show the existence of non-constant uniforml…
math.AP2015
Minimisers of the Allen-Cahn equation and the asymptotic Plateau problem on hyperbolic groups
Blaz Mramor
We investigate the existence of non-constant uniformly-bounded minimal solutions of the Allen-Cahn equation on a Gromov-hyperbolic group. We show that whenever the Laplace term in…