Document Type
Article
Publication Date
9-12-2025
Keywords
MINKOWSKI-FIREY THEORY, AFFINE SURFACE, INVARIANT VALUATIONS, APPROXIMATION, INEQUALITIES, SETS
Abstract
Three new combinations of convex bodies are introduced and studied: the fiber, chord, and graph combinations. These combinations are defined in terms of the fibers and graphs of pairs of convex bodies, and each operation generalizes the classical Steiner symmetral, albeit in different ways. For the fiber and chord combinations, we derive Brunn-Minkowski-type inequalities and the corresponding Minkowski's first inequalities. We also prove that the general affine surface areas are concave (respectively, convex) with respect to the graph sum, thereby generalizing fundamental results of Ye (Indiana Univ. Math. J. 14 (2014), 1-19) on the monotonicity of the general affine surface areas under Steiner symmetrization. As an application, we deduce a corresponding Minkowski's first inequality for the affine surface area of a graph combination of convex bodies.
Citation
Hoehner, S. and Xing, S. (2025), New fiber and graph combinations of convex bodies. Mathematika, 71: e70043. https://doi.org/10.1112/mtk.70043
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This work is licensed under a Creative Commons Attribution 4.0 International License.
Comments
Web of Science
Wiley