Intersection Bodies in R4
نویسندگان
چکیده
منابع مشابه
Intersection Bodies and Valuations
All GL (n) covariant star-body-valued valuations on convex polytopes are completely classified. It is shown that there is a unique nontrivial such valuation. This valuation turns out to be the so-called “intersection operator”—an operator that played a critical role in the solution of the Busemann-Petty problem. Introduction. A function Z defined on the set K of convex bodies (that is, of conve...
متن کاملComplex intersection bodies
We introduce complex intersection bodies and show that their properties and applications are similar to those of their real counterparts. In particular, we generalize Busemann’s theorem to the complex case by proving that complex intersection bodies of symmetric complex convex bodies are also convex. Other results include stability in the complex Busemann-Petty problem for arbitrary measures an...
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In this paper, we introduce a new concept of volumes difference function of the projection and intersection bodies. Following this, we establish the Minkowski and Brunn-Minkowski inequalities for volumes difference function of the projection and intersection bodies.
متن کاملINTERSECTION BODIES AND Lp-SPACES
In this talk we discuss a new connection between convex geometry and the theory of Lp-spaces. It appears that intersection bodies, one the main objects of convex geometry, are directly related to the concept of embedding of normed spaces in Lp with p < 0. This allows to get new geometric results by extending different facts about Lp-spaces to negative values of p. We present several application...
متن کاملIsomorphic Properties of Intersection Bodies
We study isomorphic properties of two generalizations of intersection bodies the class I k of k-intersection bodies in R and the class BPk of generalized k-intersection bodies in R. In particular, we show that all convex bodies can be in a certain sense approximated by intersection bodies, namely, if K is any symmetric convex body in R and 1 6 k 6 n− 1 then the outer volume ratio distance from ...
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ژورنال
عنوان ژورنال: Advances in Mathematics
سال: 1998
ISSN: 0001-8708
DOI: 10.1006/aima.1998.1718