In: Mathematische Zeitschrift, 2015, vol. 281, no. 1-2, p. 379-393
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In: Geometriae Dedicata, 2015, vol. 175, no. 1, p. 281-307
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In: The Journal of Geometric Analysis, 2015, vol. 25, no. 4, p. 2590-2616
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In: International Mathematics Research Notices, 2017, vol. 2017, no. 8, p. 2367-2401
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In: Advances in Calculus of Variations, 2017, vol. 10, no. 4, p. 407-421
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In: Journal für die reine und angewandte Mathematik, 2020, vol. 2020, no. 763, p. 79–109
The Dehn function measures the area of minimal discs that fill closed curves in a space; it is an important invariant in analysis, geometry, and geometric group theory. There are several equivalent ways to define the Dehn function, varying according to the type of disc used. In this paper, we introduce a new definition of the Dehn function and use it to prove several theorems. First, we...
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In: Annales de l’Institut Henri Poincaré, Probabilités et Statistiques, 2020, vol. 56, no. 4, p. 2281–2300
We consider a self-avoiding walk model (SAW) on the faces of the square lattice Z2. This walk can traverse the same face twice, but crosses any edge at most once. The weight of a walk is a product of local weights: each square visited by the walk yields a weight that depends on the way the walk passes through it. The local weights are parametrised by angles θ∈[π3,2π3] and satisfy the...
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In: Bernoulli, 2020, vol. 26, no. 3, p. 1665–1705
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In: The Journal of Geometric Analysis, 2020, p. -
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In: Calculus of Variations and Partial Differential Equations, 2020, vol. 59, no. 5, p. 177
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...
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