منابع مشابه
Inequalities for Mixed Complex Projection Bodies
Complex projection bodies were introduced by Abardia and Bernig, recently. In this paper some geometric inequalities for mixed complex projection bodies which are analogs of inequalities for mixed real projection bodies are established.
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Let Π be the projection operator, which maps every polytope to its projection body. It is well known that Π maps the set of polytopes, P, in R into P, that it is a valuation, and that for every P ∈ P, ΠP is affinely associated to P . It is shown that these properties characterize the projection operator Π. This proves a conjecture by Lutwak. Let Kn denote the set of convex bodies (i.e., of comp...
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As Schneider [50] observes, the classical Brunn-Minkowski theory had its origin at the turn of the 19th into the 20th century, when Minkowski joined a method of combining convex bodies (which became known as Minkowski addition) with that of ordinary volume. One of the core concepts that Minkowski introduced within the Brunn-Minkowski theory is that of projection body (precise definitions to fol...
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ژورنال
عنوان ژورنال: Open Mathematics
سال: 2020
ISSN: 2391-5455
DOI: 10.1515/math-2020-0055