6533b7d5fe1ef96bd12652de
RESEARCH PRODUCT
Nonsymmetric conical upper density and $k$-porosity
Ville SuomalaAntti Käenmäkisubject
Scale (ratio)Applied MathematicsGeneral Mathematics010102 general mathematicsMathematicsofComputing_GENERALGeometryConical surface01 natural sciencesUpper and lower bounds010104 statistics & probabilityMathematics - Classical Analysis and ODEsHausdorff dimensionClassical Analysis and ODEs (math.CA)FOS: MathematicsHausdorff measure0101 mathematicsPorosityMathematicsdescription
We study how the Hausdorff measure is distributed in nonsymmetric narrow cones in R n \mathbb {R}^n . As an application, we find an upper bound close to n − k n-k for the Hausdorff dimension of sets with large k k -porosity. With k k -porous sets we mean sets which have holes in k k different directions on every small scale.
| year | journal | country | edition | language |
|---|---|---|---|---|
| 2017-01-30 |