Bounding the integral of powered i-th mean curvatures

  1. David Alonso 1
  2. María A. Hernández Cifre 2
  3. Antonio R. Martínez Fernández 2
  1. 1 Universidad de Zaragoza
    info

    Universidad de Zaragoza

    Zaragoza, España

    ROR https://ror.org/012a91z28

  2. 2 Universidad de Murcia
    info

    Universidad de Murcia

    Murcia, España

    ROR https://ror.org/03p3aeb86

Revista:
Revista matemática iberoamericana

ISSN: 0213-2230

Año de publicación: 2017

Volumen: 33

Número: 4

Páginas: 1197-1218

Tipo: Artículo

DOI: 10.4171/RMI/968 DIALNET GOOGLE SCHOLAR

Otras publicaciones en: Revista matemática iberoamericana

Resumen

We get estimates for the integrals of powered i-th mean curvatures, 1≤i≤n−1, of compact and convex hypersurfaces, in terms of the quermaß integrals of the corresponding C2+ convex bodies. These bounds will be obtained as consequences of a most general result for functions defined on a general probability space. From this result, similar estimates for the integrals of any convex transformation of the elementary symmetric functions of the radii of curvature of C2+ convex bodies will be also proved, both, in terms of the quermaß integrals, and of the roots of their Steiner polynomials. Finally, the radial function is considered, and estimates of the corresponding integrals are obtained in terms of the dual quermaß integrals.

Fuente de los datos: Dialnet