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The rectifiability-dimension conjecture for measures satisfying linear PDE constraints

Let

beanbe an

-free measure, and let

betherectifiabilitydimensiondefinedbybe the rectifiability dimension defined by ∗∗Rectifiability−dimensionconjecture.∗∗TheHausdorffdimensionof**Rectifiability-dimension conjecture.** The Hausdorff dimension of

satisfies

This would improve the known lower bound involving

tothepotentiallylargerrectifiabilitydimensionto the potentially larger rectifiability dimension

. The conjecture was also advanced by Raita and appears in related work cited by the authors.

Sources & referencesView supporting material

Primary source

Adolfo Arroyo-Rabasa, Guido De Philippis, Jonas Hirsch and Filip Rindler, “Dimensional estimates and rectifiability for measures satisfying linear PDE constraints”, arXiv:1811.01847 (2019).

geometric-measure-theorylinear-pderectifiability

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