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Title: Classification of metric measure spaces and their ends using p-harmonic functions
By seeing whether a Liouville type theorem holds for positive, bounded, and/or finite \(p\)-energy \(p\)-harmonic and \(p\)-quasiharmonic functions, we classify proper metric spaces equipped with a locally doubling measure supporting a local \(p\)-Poincaré inequality. Similar classifications have earlier been obtained for Riemann surfaces and Riemannian manifolds. We study the inclusions between these classes of metric measure spaces, and their relationship to the \(p\)-hyperbolicity of the metric space and its ends. In particular, we characterize spaces that carry nonconstant \(p\)-harmonic functions with finite \(p\)-energy as spaces having at least two well-separated \(p\)-hyperbolic sequences of sets towards infinity. We also show that every such space \(X\) has a function \(f \notin L^p(X) + \mathbf{R}\) with finite \(p\)-energy.  more » « less
Award ID(s):
2054960 1800161
NSF-PAR ID:
10349391
Author(s) / Creator(s):
; ;
Date Published:
Journal Name:
Annales Fennici Mathematici
Volume:
47
Issue:
2
ISSN:
2737-0690
Page Range / eLocation ID:
1025 to 1052
Format(s):
Medium: X
Sponsoring Org:
National Science Foundation
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