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Prime ends for domains in metric spaces
Linköping University, Department of Mathematics, Mathematics and Applied Mathematics. Linköping University, The Institute of Technology.
Linköping University, Department of Mathematics, Mathematics and Applied Mathematics. Linköping University, The Institute of Technology.ORCID iD: 0000-0002-9677-8321
Linköping University, Department of Mathematics, Mathematics and Applied Mathematics. Linköping University, The Institute of Technology.ORCID iD: 0000-0002-1238-6751
University of Cincinnati, OH USA .
2013 (English)In: Advances in Mathematics, ISSN 0001-8708, E-ISSN 1090-2082, Vol. 238, 459-505 p.Article in journal (Refereed) Published
Abstract [en]

In this paper we propose a new definition of prime ends for domains in metric spaces under rather general assumptions. We compare our prime ends to those of Caratheodory and Nakki. Modulus ends and prime ends, defined by means of the p-modulus of curve families, are also discussed and related to the prime ends. We provide characterizations of singleton prime ends and relate them to the notion of accessibility of boundary points, and introduce a topology on the prime end boundary. We also study relations between the prime end boundary and the Mazurkiewicz boundary. Generalizing the notion of John domains, we introduce almost John domains, and we investigate prime ends in the settings of John domains, almost John domains and domains which are finitely connected at the boundary.

Place, publisher, year, edition, pages
Elsevier , 2013. Vol. 238, 459-505 p.
Keyword [en]
Accessibility, Almost John domain, Capacity, Doubling measure, End, Finitely connected at the boundary, John domain, Locally connected, Mazurkiewicz distance, Metric space, p-modulus, Poincare inequality, Prime end, Uniform domain
National Category
Natural Sciences
Identifiers
URN: urn:nbn:se:liu:diva-92601DOI: 10.1016/j.aim.2013.01.014ISI: 000317089200013OAI: oai:DiVA.org:liu-92601DiVA: diva2:621706
Note

Funding Agencies|Swedish Research Council||Swedish Fulbright Commission||Charles Phelps Taft Research Center at the University of Cincinnati||Taft Research Center||Simons Foundation|200474|

Available from: 2013-05-16 Created: 2013-05-14 Last updated: 2017-12-06

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Adamowicz, TomaszBjörn, AndersBjörn, Jana

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