On the Local Convexity of Intersection Bodies of Revolution
نویسندگان
چکیده
منابع مشابه
On the local convexity of intersection bodies of revolution
One of the fundamental results regarding intersection bodies is Busemann’s theorem, which states that the intersection body of a symmetric convex body is convex. Thus, it is natural to ask how much of convexity is guaranteed under the intersection body operation. In this paper we provide several results about the (strict) improvement of convexity for intersection bodies of symmetric bodies of r...
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It is a well-known result due to Busemann that the intersection body of an origin-symmetric convex body is also convex. Koldobsky introduced the notion of k-intersection bodies. We show that the k-intersection body of an origin-symmetric convex body is not necessarily convex if k > 1.
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ژورنال
عنوان ژورنال: Canadian Journal of Mathematics
سال: 2015
ISSN: 0008-414X,1496-4279
DOI: 10.4153/cjm-2013-039-4