Space of minimal discs and its compactification
| Autor: | Paul Creutz |
|---|---|
| Rok vydání: | 2019 |
| Předmět: |
Mathematics - Differential Geometry
Pure mathematics Minimal surface Geodesic Hyperbolic geometry 010102 general mathematics Metric Geometry (math.MG) Geometric Topology (math.GT) Algebraic geometry 01 natural sciences 010101 applied mathematics Metric space Mathematics - Geometric Topology Mathematics - Analysis of PDEs Differential geometry Mathematics - Metric Geometry Differential Geometry (math.DG) FOS: Mathematics Mathematics::Metric Geometry Geometry and Topology Compactification (mathematics) 0101 mathematics Isoperimetric inequality Mathematics Analysis of PDEs (math.AP) |
| DOI: | 10.48550/arxiv.1904.12572 |
| Popis: | We investigate the class of geodesic metric discs satisfying a uniform quadratic isoperimetric inequality and uniform bounds on the length of the boundary circle. We show that the closure of this class as a subset of Gromov-Hausdorff space is intimately related to the class of geodesic metric disc retracts satisfying comparable bounds. This kind of discs naturally come up in the context of the solution of Plateau's problem in metric spaces by Lytchak and Wenger as generalizations of minimal surfaces. Comment: 13 pages |
| Databáze: | OpenAIRE |
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