Space of minimal discs and its compactification
P Creutz - Geometriae Dedicata, 2021 - Springer
Geometriae Dedicata, 2021•Springer
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.
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.
Abstract
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.
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