We give a simple criterion on the set of probability tangent measures Tan(μ, x) of a positive Radon measure μ, which yields lower bounds on the Hausdorff dimension of μ. As an application, we give an elementary and purely algebraic proof of the sharp Hausdorff dimension lower bounds for first-order linear PDE-constrained measures; bounds for closed (measure) differential forms and normal currents are further discussed. A weak structure theorem in the spirit of [Ann. Math. 184(3) (2016), pp. 1017-1039] is also discussed for such measures.
An elementary approach to the dimension of measures satisfying a first-order linear PDE constraint
Arroyo-Rabasa Adolfo
2020-01-01
Abstract
We give a simple criterion on the set of probability tangent measures Tan(μ, x) of a positive Radon measure μ, which yields lower bounds on the Hausdorff dimension of μ. As an application, we give an elementary and purely algebraic proof of the sharp Hausdorff dimension lower bounds for first-order linear PDE-constrained measures; bounds for closed (measure) differential forms and normal currents are further discussed. A weak structure theorem in the spirit of [Ann. Math. 184(3) (2016), pp. 1017-1039] is also discussed for such measures.File in questo prodotto:
Non ci sono file associati a questo prodotto.
I documenti in IRIS sono protetti da copyright e tutti i diritti sono riservati, salvo diversa indicazione.
