Minkowski valuations under volume constraints

@article{AbardiaEvequoz2016MinkowskiVU,
  title={Minkowski valuations under volume constraints},
  author={J. Abardia-Ev'equoz and A. Colesanti and E. S. G'omez},
  journal={arXiv: Metric Geometry},
  year={2016}
}
  • J. Abardia-Ev'equoz, A. Colesanti, E. S. G'omez
  • Published 2016
  • Mathematics
  • arXiv: Metric Geometry
  • We provide a description of the space of continuous and translation invariant Minkowski valuations $\Phi:\mathcal{K}^n\to\mathcal{K}^n$ for which there is an upper and a lower bound for the volume of $\Phi(K)$ in terms of the volume of the convex body $K$ itself. Although no invariance with respect to a group acting on the space of convex bodies is imposed, we prove that only two types of operators appear: a family of operators having only cylinders over $(n-1)$-dimensional convex bodies as… CONTINUE READING

    References

    Publications referenced by this paper.
    SHOWING 1-10 OF 89 REFERENCES
    Valuations on convex bodies
    133
    Equivariant endomorphisms of the space of convex bodies
    45
    A classification of SL.n/ invariant valuations
    257
    Minkowski Valuations
    • Minkowski Valuations
    • 2004
    120
    Valuations and Surface Area Measures
    49
    Valuations on Sobolev spaces
    58
    Even valuations on convex bodies
    83
    Integral geometry of complex space forms
    52