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Marisa Zymonopoulou

Publications and source records attributed to Marisa Zymonopoulou.

5 recordsLinked to original sources
arXiv2015

Intersection Bodies with Certain Symmetries

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 of orthogonal transformations, generalizing complex and quaternionic convex bodies. We conduct a systematic study of sections of bodies with symmetries of this type, with the emphasis on problems of the Busemann-Petty type and hyperplane inequalities. The main role belongs to the class of intersection bodies with symmetries.

math.FA↗
arXiv2008

A note on the Busemann-Petty problem for bodies of certain invariance

The Busemann-Petty problem asks whether origin symmetric convex bodies in $\R^n$ with smaller hyperplane sections necessarily have smaller volume. The answer is affirmative if $n\leq 3$ and negative if $n\geq 4.$ We consider a class of convex bodies that have a certain invariance property with respect to their ordered k-tuples of coordinates in $\R^{kn}$ and prove the corresponding problem.

math.FA↗
arXiv2008

The modified complex Busemann-Petty problem on sections of convex bodies

Since the answer to the complex Busemann-Petty problem is negative in most dimensions, it is natural to ask what conditions on the (n-1)-dimensional volumes of the central sections of complex convex bodies with complex hyperplanes allow to compare the n-dimensional volumes. In this article we give necessary conditions on the section function in order to obtain an affirmative answer in all dimensions.

math.FA↗
arXiv2008

The complex Busemann-Petty problem for arbitrary measures

The complex Busemann-Petty problem asks whether origin symmetric convex bodies in C^n with smaller central hyperplane sections necessarily have smaller volume. The answer is affirmative if n\leq 3 and negative if n\geq 4. In this article we show that the answer remains the same if the volume is replaced by an "almost" arbitrary measure. This result is the complex analogue of Zvavitch's generalization to arbitrary measures of the original real Busemann-Petty problem.

math.FA↗