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This note details how a recent structure theorem for normal $1$-currents proved by the first and third author allows to prove a conjecture of Cheeger concerning the structure of Lipschitz differentiability spaces.
Sur l’ensemble des points de non-dérivabilité d’une fonction continue
Z. Zahorski · 1946
Earlier work this paper cites.
Geometric measure theory
H. Federer · 1969
Earlier work this paper cites.
Differentiability of lipschitz functions on banach spaces
D. Preiss · 1990
Earlier work this paper cites.
Rank one property for derivatives of functions with bounded variation
G. Alberti · 1993
Earlier work this paper cites.
Decomposition of solenoidal vector charges into elementary solenoids, and the structure of normal one-dimensional flows
S. K. Smirnov · 1994
Earlier work this paper cites.
Differentiability of Lipschitz functions on metric measure spaces
J. Cheeger · 1999
Earlier work this paper cites.
A differentiable structure for metric measure spaces
S. Keith · 2004
Earlier work this paper cites.
Structure of null sets in the plane and applications
G. Alberti, M. Csörnyei, and D. Preiss · 2005
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Gradient flows in metric spaces and in the space of probability measures
L. Ambrosio, N. Gigli, and G. Savaré · 2005
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On the differentiability of Lipschitz maps from metric measure spaces to Banach spaces
J. Cheeger and B. Kleiner · 2006
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Differentiability of Lipschitz maps from metric measure spaces to Banach spaces with the Radon-Nikodým property
J. Cheeger and B. Kleiner · 2009
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Differentiability of lipschitz functions, structure of null sets, and other problems
G. Alberti, M. Csörnyei, and D. Preiss · 2010
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Product formulas for measures and applications to analysis and geometry, 2011
Structure of measures in Lipschitz differentiability spaces
D. Bate · 2015
Later among the works it cites.
Differentiability of Lipschitz functions in Lebesgue null sets
D. Preiss and G. Speight · 2015
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On the differentiability of lipschitz functions with respect to measures in the Euclidean space
G. Alberti and A. Marchese · 2016
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On the structure of 𝒜 \mathcal{A} -free measures and applications
G. De Philippis and F. Rindler · 2016
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Behaviour of the reference measure on 𝖱𝖢𝖣 \mathsf{RCD} spaces under charts
N. Gigli and E. Pasqualetto · 2016
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P. Jones · 2011
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Rigidity of derivations in the plane and in metric measure spaces
J. Gong · 2012
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M. Kell and A. Mondino · 2016
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Derivations and Alberti representations
A. Schioppa · 2016
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