Exponential reweighting of measures under Bonk-Heinonen-Koskela uniformization and hyperbolization preserves local doubling and Poincare inequalities, yielding a boundary-capacity characterization of the finite-energy Liouville theorem for p-harmonic functions on Gromov hyperbolic spaces.
and Shanmugalingam, N., Carleson-type estimates for p- harmonic functions and the conformal Martin boundary of John do mains in metric measure spaces, Michigan Math
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Bounded geometry and $p$-harmonic functions under uniformization and hyperbolization
Exponential reweighting of measures under Bonk-Heinonen-Koskela uniformization and hyperbolization preserves local doubling and Poincare inequalities, yielding a boundary-capacity characterization of the finite-energy Liouville theorem for p-harmonic functions on Gromov hyperbolic spaces.