Faculté des sciences

Energy and area minimizers in metric spaces

Lytchak, Alexander ; Wenger, Stefan

In: Advances in Calculus of Variations, 2016, vol. 10, no. 4, p. 407–421

We show that in the setting of proper metric spaces one obtains a solution of the classical 2-dimensional Plateau problem by minimizing the energy, as in the classical case, once a definition of area 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... Plus

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    Summary
    We show that in the setting of proper metric spaces one obtains a solution of the classical 2-dimensional Plateau problem by minimizing the energy, as in the classical case, once a definition of area 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 Hölder exponents of some area-minimizing discs.