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arXiv · 1507.02670

Energy and area minimizers in metric spaces

Alexander Lytchak·Stefan Wenger
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Abstract

We show that in the setting of proper metric spaces one obtains a solution of the classical two-dimensional Plateau problem by minimizing the energy, as in the classical case, once a definition of area (in the sense of convex geometry) has been chosen appropriately. We prove the quasi-convexity of this new definition of area. Under the assumption of a quadratic isoperimetric inequality we establish regularity results for energy minimizers and improve Hoelder exponents of some area-minimizing discs.

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Alexander Lytchak, Stefan Wenger. 2015-07-09. Energy and area minimizers in metric spaces. https://arxiv.org/abs/1507.02670

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