Journal
CALCULUS OF VARIATIONS AND PARTIAL DIFFERENTIAL EQUATIONS
Volume 59, Issue 5, Pages -Publisher
SPRINGER HEIDELBERG
DOI: 10.1007/s00526-020-01843-0
Keywords
30L10; 49Q05; 53B40
Categories
Funding
- DFG [SPP 2026]
- Vilho, Yrjo ja Kalle Vaisala Foundation (postdoc pool)
- Swiss National Science Foundation [182423]
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We find maximal representatives within equivalence classes of metric spheres. For Ahlfors regular spheres these are uniquely characterized by satisfying the seemingly unrelated notions of Sobolev-to-Lipschitz property, or volume rigidity. We also apply our construction to solutions of the Plateau problem in metric spaces and obtain a variant of the associated intrinsic disc studied by Lytchak-Wenger, which satisfies a related maximality condition.
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