A new pointwise invariant, the Point-Cross Dimension, quantifies the cumulative weighted complexity of independent directional channels through a single germ, separating directionality from isotropic dispersion.
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3 Pith papers cite this work. Polarity classification is still indexing.
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Pith papers citing it
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2026 3representative citing papers
Marstrand's projection theorem fails for the Assouad spectrum and quasi-Assouad dimension, with new almost-sure lower bounds from capacity profiles and upper bounds from tube-counting for planar sets.
Proves lower bounds for the parabolic Hausdorff dimension of orthogonal projections of Borel sets A in R^n x R onto generic m-dimensional linear subspaces.
citing papers explorer
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Point-dimension theory (part II): The point-cross dimension
A new pointwise invariant, the Point-Cross Dimension, quantifies the cumulative weighted complexity of independent directional channels through a single germ, separating directionality from isotropic dispersion.
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On the Marstrand projection theorem for the Assouad spectrum
Marstrand's projection theorem fails for the Assouad spectrum and quasi-Assouad dimension, with new almost-sure lower bounds from capacity profiles and upper bounds from tube-counting for planar sets.
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On the parabolic Hausdorff dimension of orthogonal projections
Proves lower bounds for the parabolic Hausdorff dimension of orthogonal projections of Borel sets A in R^n x R onto generic m-dimensional linear subspaces.