0000000000526387

AUTHOR

Themis Mitsis

showing 3 related works from this author

Topics in harmonic analysis

2003

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A note on the distance set problem in the plane

2001

We use a simple geometric-combinatorial argument to establish a quantitative relation between the generalized Hausdorff measure of a set and its distance set, extending a result originally due to Falconer.

Discrete mathematicsPlane (geometry)Applied MathematicsGeneral MathematicsMathematical analysisσ-finite measureMeasure (mathematics)Set (abstract data type)Simple (abstract algebra)Mathematics::Metric GeometryHausdorff measureOuter measureBorel measureMathematicsProceedings of the American Mathematical Society
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An optimal extension of Marstrand?s plane-packing theorem

2003

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.

Discrete mathematicsUnit spheresymbols.namesakePacking dimensionLebesgue measureGeneral MathematicsHausdorff dimensionsymbolsDimension functionHausdorff measureLebesgue covering dimensionEffective dimensionMathematicsArchiv der Mathematik
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