A remark on measures of sections of $L_p$-balls
Alexander Koldobsky, Alain Pajor
TL;DR
This paper extends the slicing problem to subspaces of Lp spaces for p>2 under arbitrary measures, generalizing Milman's classical result and broadening the understanding of geometric measure properties.
Contribution
It generalizes Milman's slicing problem result from volume to arbitrary measures for subspaces of Lp spaces with p>2.
Findings
Slicing problem holds for subspaces of Lp, p>2, with arbitrary measures.
Generalizes classical volume-based slicing results.
Enhances understanding of measure-based geometric properties.
Abstract
We show that the slicing problem holds true for subspaces of in the setting of arbitrary measures in place of volume. This generalizes a result of Milman for the original slicing problem.
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Taxonomy
TopicsPoint processes and geometric inequalities · Geometric Analysis and Curvature Flows · Digital Image Processing Techniques