Intrinsic structure of minimal discs in metric spaces
- Lytchak, Alexander Mathematisches Institut, Universität Köln, Germany
- Wenger, Stefan Department of Mathematics, University of Fribourg, Switzerland
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31.10.2017
Published in:
- Geometry & Topology. - 2017, vol. 22, no. 1, p. 591–644
English
We study the intrinsic structure of parametric minimal discs in metric spaces admitting a quadratic isoperimetric inequality. We associate to each minimal disc a compact, geodesic metric space whose geometric, topological, and analytic properties are controlled by the isoperimetric inequality. Its geometry can be used to control the shapes of all curves and therefore the geometry and topology of the original metric space. The class of spaces arising in this way as intrinsic minimal discs is a natural generalization of the class of Ahlfors regular discs, well-studied in analysis on metric spaces.
- Faculty
- Faculté des sciences et de médecine
- Department
- Département de Mathématiques
- Language
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- English
- Classification
- Mathematics
- License
- License undefined
- Identifiers
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- RERO DOC 309508
- DOI 10.2140/gt.2018.22.591
- Persistent URL
- https://folia.unifr.ch/unifr/documents/306725
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