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Kinematic formulas for sets defined by differences of convex functions

The result's identifiers

  • Result code in IS VaVaI

    <a href="https://www.isvavai.cz/riv?ss=detail&h=RIV%2F00216208%3A11320%2F17%3A10369099" target="_blank" >RIV/00216208:11320/17:10369099 - isvavai.cz</a>

  • Result on the web

    <a href="http://dx.doi.org/10.1016/j.aim.2017.03.003" target="_blank" >http://dx.doi.org/10.1016/j.aim.2017.03.003</a>

  • DOI - Digital Object Identifier

    <a href="http://dx.doi.org/10.1016/j.aim.2017.03.003" target="_blank" >10.1016/j.aim.2017.03.003</a>

Alternative languages

  • Result language

    angličtina

  • Original language name

    Kinematic formulas for sets defined by differences of convex functions

  • Original language description

    The class WDC(M) consists of all subsets of a smooth manifold M that may be expressed in local coordinates as sufficiently regular sublevel sets of DC (differences of convex) functions. If M is Riemannian and G is a group of isometries acting transitively on the sphere bundle SM, we define the invariant curvature measures of compact WDC subsets of M, and show that pairs of such subsets are subject to the array of kinematic formulas known to apply to smoother sets. Restricting to the case (M, = (R-d, &lt;(SO(d))over bar&gt;), this extends and subsumes Federer&apos;s theory of sets with positive reach in an essential way. The key technical point is equivalent to a sharpening of a classical theorem of Ewald, Larman, and Rogers characterizing the dimension of the set of directions of line segments lying in the boundary of a given convex body.

  • Czech name

  • Czech description

Classification

  • Type

    J<sub>imp</sub> - Article in a specialist periodical, which is included in the Web of Science database

  • CEP classification

  • OECD FORD branch

    10101 - Pure mathematics

Result continuities

  • Project

    <a href="/en/project/GA15-08218S" target="_blank" >GA15-08218S: Theory of real functions and its applications in geometry</a><br>

  • Continuities

    P - Projekt vyzkumu a vyvoje financovany z verejnych zdroju (s odkazem do CEP)

Others

  • Publication year

    2017

  • Confidentiality

    S - Úplné a pravdivé údaje o projektu nepodléhají ochraně podle zvláštních právních předpisů

Data specific for result type

  • Name of the periodical

    Advances in Mathematics

  • ISSN

    0001-8708

  • e-ISSN

  • Volume of the periodical

    311

  • Issue of the periodical within the volume

    April

  • Country of publishing house

    US - UNITED STATES

  • Number of pages

    37

  • Pages from-to

    796-832

  • UT code for WoS article

    000398982000022

  • EID of the result in the Scopus database

    2-s2.0-85015180446