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Fractal Geometry and Stochastics VIp-Hyperbolicity of Ends and Families of Paths in Metric Spaces

Fractal Geometry and Stochastics VI: p-Hyperbolicity of Ends and Families of Paths in Metric Spaces [The purpose of this note is to give an expository survey on the notions of p-parabolicity and p-hyperbolicity of metric measure spaces of locally bounded geometry. These notions are extensions of the notions of recurrence and transience to non-linear operators such as the p-Laplacian (with the standard Laplacian or the 2-Laplacian associated with recurrence and transience behaviors). We discuss characterizations of these notions in terms of potential theory and in terms of moduli of families of paths in the metric space.] http://www.deepdyve.com/assets/images/DeepDyve-Logo-lg.png

Fractal Geometry and Stochastics VIp-Hyperbolicity of Ends and Families of Paths in Metric Spaces

Part of the Progress in Probability Book Series (volume 76)
Editors: Freiberg, Uta; Hambly, Ben; Hinz, Michael; Winter, Steffen
Shanmugalingam, Nageswari
Fractal Geometry and Stochastics VI — Mar 24, 2021
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References (27)

Publisher
Springer International Publishing
Copyright
© Springer Nature Switzerland AG 2021
ISBN
978-3-030-59648-4
Pages
191 –205
DOI
10.1007/978-3-030-59649-1_8
Publisher site
See Chapter on Publisher Site

Abstract

[The purpose of this note is to give an expository survey on the notions of p-parabolicity and p-hyperbolicity of metric measure spaces of locally bounded geometry. These notions are extensions of the notions of recurrence and transience to non-linear operators such as the p-Laplacian (with the standard Laplacian or the 2-Laplacian associated with recurrence and transience behaviors). We discuss characterizations of these notions in terms of potential theory and in terms of moduli of families of paths in the metric space.]

Published: Mar 24, 2021

Keywords: Recurrence; p -hyperbolic; Singular function; Modulus of curve families; Ends; Primary: 31E05; Secondary: 43A85; 65M80

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