Energy and area minimizers in metric spaces
Lytchak, Alexander ; Wenger, Stefan
In: Advances in Calculus of Variations, 2017, vol. 10, no. 4, p. 407-421
Ajouter à la liste personnelle- 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.