37 citations · 42 across the 6 of their papers we have counts for
7 papers
Intersection Bodies with Certain Symmetries
Susanna Dann, Marisa Zymonopoulou
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 diagona…
Complex Intersection Bodies
A. Koldobsky, G. Paouris, M. Zymonopoulou
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 th…
Isomorphic properties of Intersection bodies
A. Koldobsky, G. Paouris, M. Zymonopoulou
We study isomorphic properties of two generalizations of intersection bodies, the class of k-intersection bodies and the class of generalized k-intersection bodies. We also show th…
Positive Definite Distributions and Normed Spaces
Nigel J. Kalton, Marisa Zymonopoulou
We answer a question of Alex Koldobsky on isometric embeddings of finite dimensional normed spaces.
A note on the Busemann-Petty problem for bodies of certain invariance
Marisa Zymonopoulou
The Busemann-Petty problem asks whether origin symmetric convex bodies in with smaller hyperplane sections necessarily have smaller volume. The answer is affirmative if $n\l…
The complex Busemann-Petty problem for arbitrary measures
Marisa Zymonopoulou
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 affirm…