Potential Theory on Gromov Hyperbolic Spaces
Gromov hyperbolic spaces have become an essential concept in geometry, topology and group theory. Herewe extend Ancona's potential theory on Gromov hyperbolic manifolds and graphs of bounded geometry to a large class of Schrödinger operators on Gromov hyperbolic metric measure spaces, unifying...
| Verfasser: | |
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| FB/Einrichtung: | FB 10: Mathematik und Informatik |
| Dokumenttypen: | Artikel |
| Medientypen: | Text |
| Erscheinungsdatum: | 2022 |
| Publikation in MIAMI: | 17.01.2023 |
| Datum der letzten Änderung: | 03.11.2023 |
| Angaben zur Ausgabe: | [Electronic ed.] |
| Quelle: | Analysis and Geometry in Metric Spaces 10 (2022) 1, 394–431 |
| Schlagwörter: | Gromov Hyperbolic Space; Dirichlet Form; Schrödinger Operator; Boundary Harnack Inequality; Gromov Boundary; Martin Boundary |
| Fachgebiet (DDC): | 510: Mathematik
515: Analysis 516: Geometrie |
| Lizenz: | CC BY 4.0 |
| Sprache: | English |
| Förderung: | Finanziert durch den Open-Access-Publikationsfonds der Universität Münster. |
| Format: | PDF-Dokument |
| URN: | urn:nbn:de:hbz:6-31059668102 |
| Weitere Identifikatoren: | DOI: 10.17879/41059541463 |
| Permalink: | https://nbn-resolving.de/urn:nbn:de:hbz:6-31059668102 |
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| Onlinezugriff: | 10.1515_agms-2022-0147.pdf |
Gromov hyperbolic spaces have become an essential concept in geometry, topology and group theory. Herewe extend Ancona's potential theory on Gromov hyperbolic manifolds and graphs of bounded geometry to a large class of Schrödinger operators on Gromov hyperbolic metric measure spaces, unifying these settings in a common framework ready for applications to singular spaces such as RCD spaces or minimal hypersurfaces. Results include boundary Harnack inequalities and a complete classification of positive harmonic functions in terms of the Martin boundary which is identified with the geometric Gromov boundary.