Convergence of symmetrization processes

نویسندگان

چکیده

Steiner and Schwarz symmetrizations, their most important relatives, the Minkowski, Minkowski-Blaschke, fiber, inner rotational, outer rotational are investigated. The focus is on convergence of successive symmetrals with respect to a sequence $i$-dimensional subspaces $\mathbb{R}^n$. Such called universal for family sets if any set in converge ball center at origin. New sequences main all valid dimensions $i$ subspaces, found, by combining two groups results. first, published separately, provides finite ${\mathcal{F}}$ such that reflection symmetry (or symmetry) each subspace implies full symmetry. In second, proved here, theorem Klain symmetrization extended Schwarz, fiber showing drawn from compact convex symmetric appearing infinitely often sequence. It also Steiner, Minkowski class only it sets, Klain's shown hold sets.

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ژورنال

عنوان ژورنال: Indiana University Mathematics Journal

سال: 2022

ISSN: ['1943-5258', '0022-2518', '1943-5266']

DOI: https://doi.org/10.1512/iumj.2022.71.9170