6533b86ffe1ef96bd12ce5d0
RESEARCH PRODUCT
An optimal extension of Marstrand?s plane-packing theorem
Themis MitsisThemis Mitsissubject
Discrete mathematicsUnit spheresymbols.namesakePacking dimensionLebesgue measureGeneral MathematicsHausdorff dimensionsymbolsDimension functionHausdorff measureLebesgue covering dimensionEffective dimensionMathematicsdescription
We prove that if F is a subset of the 2-dimensional unit sphere in $\mathbb{R}^3$, with Hausdorff dimension strictly greater than 1, and E is a subset of $\mathbb{R}^3$ such that for each $e \in F$, E contains a plane perpendicular to the vector e, then E must have positive 3-dimensional Lebesgue measure.
| year | journal | country | edition | language |
|---|---|---|---|---|
| 2003-08-01 | Archiv der Mathematik |