10 papers
Complex homothetic sections and projections through a Helly type Theorem for cosets of
Jorge Luis Arocha, Javier Bracho, Luis Montejano
We prove that two closed subsets of complex space $\C^n$ with corresponding complex homothetic sections (projections) are complex homothetic. The proof uses a new Helly-type theore…
An overview of complex ellipsoids
Jorge Luis Arocha, Javier Bracho, Luis Montejano
An ellipsoid is the image of a ball under an affine transformation. If this affine transformation is over the complex numbers, we refer to it as a complex ellipsoid. Characterizati…
Reflections of convex bodies and their sections
Jorge L. Arocha, Javier Bracho, Luis Montejano
The purpose of this paper is to study the reflections of a convex body. In particular, we are interested in orthogonal reflections of its sections that can be extended to reflectio…
Complex ellipsoids and complex symmetry
Jorge Arocha, Javier Bracho, Luis Montejano
Several characterizations of complex ellipsoids among convex bodies in Cn, in terms of their sections and projections are proved. Characterizing complex symmetry in similar terms i…
Reconstructing triangulations of 3-manifolds from their intersection matrix
Jorge L. Arocha, Jorge Fernández-Hidalgo
The intersection matrix of a simplicial complex has entries equal to the rank of the intersection of its facets. In [1] the authors prove the intersection matrix is enough to deter…
Extremal inscribed and circumscribed complex ellipsoids
Jorge L. Arocha, Javier Bracho, Luis Montejano
We prove that if a convex set in Cn contains two inscribed complex ellipsoid of maximal volume then one is a translate of the other. On the other hand, the circumscribed complex el…