Curvature Densities of Self-Similar Sets

Result code in IS VaVaI

<a href="https://www.isvavai.cz/riv?ss=detail&h=RIV%2F00216208%3A11320%2F12%3A10140181" target="_blank" >RIV/00216208:11320/12:10140181 - isvavai.cz</a>

Result on the web

<a href="http://dx.doi.org/10.1512/iumj.2012.61.4681" target="_blank" >http://dx.doi.org/10.1512/iumj.2012.61.4681</a>

DOI - Digital Object Identifier

<a href="http://dx.doi.org/10.1512/iumj.2012.61.4681" target="_blank" >10.1512/iumj.2012.61.4681</a>

Result language

angličtina

Original language name

Curvature Densities of Self-Similar Sets

Original language description

For a large class of self-similar sets F in R-d, analogues of the higher-order mean curvatures of differentiable sub-manifolds are introduced-in particular, the fractal Gauss-type curvature. They are shown to be the densities of associated fractal curvature measures, which are all multiples of the corresponding Hausdorff measures on F, due to its self-similarity. This local approach based on ergodic theory for an associated dynamical system enables us to extend former total curvature results.

Czech name

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Czech description

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Type

J_x - Unclassified - Peer-reviewed scientific article (Jimp, Jsc and Jost)

CEP classification

BA - General mathematics

OECD FORD branch

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Project

<a href="/en/project/GCP201%2F10%2FJ039" target="_blank" >GCP201/10/J039: Curvature measures and integral geometry</a><br>

Continuities

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

Publication year

2012

Confidentiality

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

Name of the periodical

Indiana University Mathematics Journal

ISSN

0022-2518

e-ISSN

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Volume of the periodical

61

Issue of the periodical within the volume

4

Country of publishing house

US - UNITED STATES

Number of pages

25

Pages from-to

1425-1449

UT code for WoS article

000323187700003

EID of the result in the Scopus database

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