Mixed curvature measures of translative integral geometry

Kód výsledku v IS VaVaI

<a href="https://www.isvavai.cz/riv?ss=detail&h=RIV%2F00216208%3A11320%2F18%3A10384531" target="_blank" >RIV/00216208:11320/18:10384531 - isvavai.cz</a>

Výsledek na webu

<a href="https://doi.org/10.1007/s10711-017-0278-1" target="_blank" >https://doi.org/10.1007/s10711-017-0278-1</a>

DOI - Digital Object Identifier

<a href="http://dx.doi.org/10.1007/s10711-017-0278-1" target="_blank" >10.1007/s10711-017-0278-1</a>

Jazyk výsledku

angličtina

Název v původním jazyce

Mixed curvature measures of translative integral geometry

Popis výsledku v původním jazyce

The curvature measures of a set X with singularities are measures concentrated on the normal bundle of X, which describe the local geometry of the set X. For given finitely many convex bodies or, more generally, sets with positive reach, the translative integral formula for curvature measures relates the integral mean of the curvature measures of the intersections of the given sets, one fixed and the others translated, to the mixed curvature measures of the given sets. In the case of two sets of positive reach, a representation of these mixed measures in terms of generalized curvatures, defined on the normal bundles of the sets, is known. For more than two sets, a description of mixed curvature measures in terms of rectifiable currents has been derived previously. Here we provide a representation of mixed curvature measures of sets with positive reach based on generalized curvatures. The special case of convex polyhedra is treated in detail.

Název v anglickém jazyce

Mixed curvature measures of translative integral geometry

Popis výsledku anglicky

The curvature measures of a set X with singularities are measures concentrated on the normal bundle of X, which describe the local geometry of the set X. For given finitely many convex bodies or, more generally, sets with positive reach, the translative integral formula for curvature measures relates the integral mean of the curvature measures of the intersections of the given sets, one fixed and the others translated, to the mixed curvature measures of the given sets. In the case of two sets of positive reach, a representation of these mixed measures in terms of generalized curvatures, defined on the normal bundles of the sets, is known. For more than two sets, a description of mixed curvature measures in terms of rectifiable currents has been derived previously. Here we provide a representation of mixed curvature measures of sets with positive reach based on generalized curvatures. The special case of convex polyhedra is treated in detail.

Druh

J_imp - Článek v periodiku v databázi Web of Science

CEP obor

—

OECD FORD obor

10101 - Pure mathematics

Projekt

<a href="/cs/project/GA15-08218S" target="_blank" >GA15-08218S: Teorie reálných funkcí a její aplikace v geometrii</a><br>

Návaznosti

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

Rok uplatnění

2018

Kód důvěrnosti údajů

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

Název periodika

Geometriae Dedicata

ISSN

0046-5755

e-ISSN

—

Svazek periodika

195

Číslo periodika v rámci svazku

1

Stát vydavatele periodika

NL - Nizozemsko

Počet stran výsledku

20

Strana od-do

101-120

Kód UT WoS článku

000437122700006

EID výsledku v databázi Scopus

2-s2.0-85027718482