A tight estimate for the waist of the ball

@article{Akopyan2016ATE,
  title={A tight estimate for the waist of the ball},
  author={A. Akopyan and R. Karasev},
  journal={arXiv: Metric Geometry},
  year={2016}
}
  • A. Akopyan, R. Karasev
  • Published 2016
  • Mathematics
  • arXiv: Metric Geometry
  • We answer a question of M. Gromov on the waist of the unit ball. In [3] Gromov proved that for any continuous map f : R → R, where we fix a Gauss measure γ in R, there exists a fiber f−1(y) such that any its t-neighborhood has measure γ(f−1(y) + t) (we denote t-neighborhood simply by +t) at least the measure of a t-neighborhood of a linear subspace Rn−k ⊂ R. He also sketched the proof of a similar fact for the round sphere S with its uniform measure, later presented in a detailed form by… CONTINUE READING
    Gromov's waist of non-radial Gaussian measures and radial non-Gaussian measures
    1
    Waist of balls in hyperbolic and spherical spaces
    2
    Lower and upper bounds for the waists of different spaces
    9

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