Complex Intersection Bodies

Details Complex Intersection Bodies Complex Intersection Bodies

2012-01-02

arxiv.org/abs/1201.0437v1

Mathematics

Functional Analysis

Scientific paper

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 theorem to the complex case by proving that complex intersection bodies of symmetric complex convex bodies are also convex. Other results include stability in the complex Busemann-Petty problem for arbitrary measures and the corresponding hyperplane inequality for measures of complex intersection bodies.

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