On the structure of A-free measures and applications

By Guido De Philippis, Filip Rindler. 2016

162 citations recorded by the source corpus.

Subfields: Applied Mathematics, Mathematical Physics

View Paper: https://www.semanticscholar.org/paper/69306409cf18bd7c8c8021fcc66b46723e4fc8bf

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In Applied Mathematics

In Mathematical Physics

Citations in the corpus

Behaviour of the reference measure on $\sf RCD$ spaces under charts (2016, methodology): “emma 1.14 in [6] does not hold on weighted Riemannian manifolds, and a fortiori does not hold on RCDspaces. Our argument, instead, uses as key tool the following recent result by De Philippis-Rindler [8]: Theorem 1.1. Let T1 = −→ T1kT1k,...,Td = −→ TdkTdk be one dimensional normal currents in Rd and”
On a conjecture of Cheeger (2016, methodology): “btained by combining the results of [Alb93] and [AM16], see [AM16, Remark 6.2 (iv)]. Recently, a result concerning the singular structure of measures satisfying a diﬀerential constraint was proved in [DR16]. When combined with the main result of [AM16], this proves the weak converse of Rademacher’s ”
On the volume measure of non-smooth spaces with Ricci curvature bounded below (2016, methodology): “5 proved in [19], while in [20] the absolute continuity of the measure is achieved by a slightly different argument involving one-dimensional currents.”
Rectifiability of Varifolds with Locally Bounded First Variation with Respect to Anisotropic Surface Energies (2016, unknown): “A key step is then to show that kV k H d : this is achieved by using ideas borrowed from [3, 14].”
Short-time behavior of the heat kernel and Weyl's law on $RCD^*(K, N)$-spaces (2017, unknown): “More recently, building on [18], more than one group of authors have shown thatm-almost all ofRi can be covered by bi-Lipschitz charts defined in subsets of Ri , and that the restriction of the reference measure to each Ri is absolutely continuous w.”
Lower semicontinuity and relaxation of linear-growth integral functionals under PDE constraints (2017, methodology): “Themain result of [10] asserts that the polar vector of the singular part of anA-freemeasure μ necessarily has to lie in ΛA: Theorem 2.”