Boundary Growth Rates and Exceptional Sets for Superharmonic Functions on the Real Hyperbolic Ball

Boundary Growth Rates and Exceptional Sets for Superharmonic Functions on the Real Hyperbolic Ball

We present a sharp upper bound of the Hausdorff dimension of an exceptional set in the unit sphere where a positive superharmonic function with respect to the hyperbolic Laplacian on the unit ball blows up faster than a prescribed order.

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Veröffentlicht in:The Journal of Geometric Analysis 2021-11, Vol.31 (11), p.10586-10602
1. Verfasser: Hirata, Kentaro
Format: Artikel
Sprache:eng
Schlagworte:
Abstract Harmonic Analysis
Convex and Discrete Geometry
Differential Geometry
Dynamical Systems and Ergodic Theory
Fourier Analysis
Geometry
Global Analysis and Analysis on Manifolds
Harmonic functions
Mathematics
Mathematics and Statistics
Upper bounds
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Beschreibung
Zusammenfassung:We present a sharp upper bound of the Hausdorff dimension of an exceptional set in the unit sphere where a positive superharmonic function with respect to the hyperbolic Laplacian on the unit ball blows up faster than a prescribed order.
ISSN:1050-6926
1559-002X
DOI:10.1007/s12220-021-00657-6