2023
DOI: 10.48550/arxiv.2302.11973
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Fixed Points of Mean Section Operators

Abstract: We characterize rotation equivariant bounded linear operators from C(S n−1 ) to C 2 (S n−1 ) by the mass distribution of the spherical Laplacian of their kernel function on small polar caps. Using this characterization, we show that every continuous, homogeneous, translation invariant, and rotation equivariant Minkowski valuation Φ that is weakly monotone maps the space of convex bodies with a C 2 support function into itself. As an application, we prove that if Φ is in addition even or a mean section operator… Show more

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