The unit ball is an attractor of the intersection body operator ✩

@inproceedings{Fish2010TheUB,
  title={The unit ball is an attractor of the intersection body operator ✩},
  author={Alexander Fish and Fedor Nazarov and Dmitry Ryabogin and Artem Zvavitch},
  year={2010}
}
The intersection body of a ball is again a ball. So, the unit ball Bd ⊂ Rd is a fixed point of the intersection body operator acting on the space of all star-shaped origin symmetric bodies endowed with the Banach– Mazur distance. E. Lutwak asked if there is any other star-shaped body that satisfies this property. We show that this fixed point is a local attractor, i.e., that the iterations of the intersection body operator applied to any star-shaped origin symmetric body sufficiently close to… CONTINUE READING
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