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Let $\mu$ be a probability measure on $\mathbb{R}^n$ with a bounded density $f$. We prove that the marginals of $f$ on most subspaces are well-bounded. For product measures, studied recently by… (More)

- Susanna Dann
- 2011

The Busemann-Petty problem asks whether origin-symmetric convex bodies in real Euclidean n-space with smaller central hyperplane sections necessarily have smaller volume. The answer is affirmative… (More)

One of the important questions related to any integral transform on a manifold M or on a homogeneous space G/K is the description of the image of a given space of functions. If M=G/K, where (G,K) is… (More)

Intersection bodies were introduced by E. Lutwak in 1988 in his celebrated paper [31] in connection with the Busemann-Petty problem. We recall that an origin-symmetric star body K in R is an… (More)

- Markus Ausserhofer, Susanna Dann, Zsolt Lángi, Géza Tóth
- Discrete Applied Mathematics
- 2017

A convex polygon Q is circumscribed about a convex polygon P if every vertex of P lies on at least one side of Q. We present an algorithm for finding a maximum area convex polygon circumscribed about… (More)

- Susanna Dann
- Adv. Appl. Math.
- 2014

The lower dimensional Busemann-Petty problem asks whether origin-symmetric convex bodies in R^n with smaller volume of all k-dimensional sections necessarily have smaller volume. The answer is… (More)

The average section functional as(K) of a star body in Rn is the average volume of its central hyperplane sections: $$as\left( k \right) = \int_{{S^{n - 1}}} {\left| {K \cap {\xi ^ \bot }} \right|}… (More)

Abstract In this paper we study how certain symmetries of convex bodies affect their geometric properties. In particular, we consider the impact of symmetries generated by the block diagonal subgroup… (More)