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- W4320342336 abstract "This article belongs to the area of geometric tomography, which is the study of geometric properties of solids based on data about their sections and projections. We describe a new direction in geometric tomography where different volumetric results are considered in a more general setting, with volume replaced by an arbitrary measure. Surprisingly, such a general approach works for a number of volumetric results. In particular, we discuss the Busemann-Petty problem on sections of convex bodies for arbitrary measures and the slicing problem for arbitrary measures. We present generalizations of these questions to the case of functions. A number of generalizations of questions related to projections, such as the problem of Shephard, are also discussed as well as some questions in discrete tomography." @default.
- W4320342336 created "2023-02-13" @default.
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- W4320342336 date "2023-02-08" @default.
- W4320342336 modified "2023-09-23" @default.
- W4320342336 title "Inequalities for sections and projections of convex bodies" @default.
- W4320342336 doi "https://doi.org/10.48550/arxiv.2302.04347" @default.
- W4320342336 hasPublicationYear "2023" @default.
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