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, <(SO(d))over bar>), this extends and subsumes Federer'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
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Czech description
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Classification
Type
J<sub>imp</sub> - Article in a specialist periodical, which is included in the Web of Science database
CEP classification
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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
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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