Matches in SemOpenAlex for { <https://semopenalex.org/work/W4290804702> ?p ?o ?g. }
Showing items 1 to 51 of
51
with 100 items per page.
- W4290804702 abstract "Valuations constitute a class of functionals on convex bodies which include the Euler-characteristic, the surface area, the Lebesgue-measure, and many more classical functionals. Curvature measures may be regarded as localised`` versions of valuations which yield local information about the geometry of a body's boundary. A complete classification of continuous translation-invariant $mathrm{SO}(n)$-invariant valuations and curvature measures with values in $mathbb{R}$ was obtained by Hadwiger and Schneider, respectively. More recently, characterisation results have been achieved for curvature measures with values in $operatorname{Sym}^p mathbb{R}^n$ and $operatorname{Sym}^2!Lambda^{q} mathbb{R}^n$ for $p,q geq 1$ with varying assumptions as for their invariance properties. In the present work, we classify all smooth translation-invariant $mathrm{SO}(n)$-covariant curvature measures with values in any $mathrm{SO}(n)$-representation in terms of certain differential forms on the sphere bundle $Smathbb{R}^n$ and describe their behaviour under the globalisation map. The latter result also yields a similar classification of all continuous $mathrm{SO}(n)$-covariant valuations with values in any $mathrm{SO}(n)$-representation. Furthermore, a decomposition of the space of smooth translation-invariant $mathbb{R}$-valued curvature measures as an $mathrm{SO}(n)$-representation is obtained. As a corollary, we construct an explicit basis of continuous translation-invariant $mathbb{R}$-valued valuations." @default.
- W4290804702 created "2022-08-12" @default.
- W4290804702 creator A5005957195 @default.
- W4290804702 date "2019-03-07" @default.
- W4290804702 modified "2023-09-29" @default.
- W4290804702 title "Characterisation of Valuations and Curvature Measures in Euclidean Spaces" @default.
- W4290804702 doi "https://doi.org/10.48550/arxiv.1903.03100" @default.
- W4290804702 hasPublicationYear "2019" @default.
- W4290804702 type Work @default.
- W4290804702 citedByCount "0" @default.
- W4290804702 crossrefType "posted-content" @default.
- W4290804702 hasAuthorship W4290804702A5005957195 @default.
- W4290804702 hasBestOaLocation W42908047021 @default.
- W4290804702 hasConcept C114614502 @default.
- W4290804702 hasConcept C134306372 @default.
- W4290804702 hasConcept C14158598 @default.
- W4290804702 hasConcept C190470478 @default.
- W4290804702 hasConcept C195065555 @default.
- W4290804702 hasConcept C202444582 @default.
- W4290804702 hasConcept C2524010 @default.
- W4290804702 hasConcept C2777105136 @default.
- W4290804702 hasConcept C33923547 @default.
- W4290804702 hasConcept C37914503 @default.
- W4290804702 hasConcept C9136319 @default.
- W4290804702 hasConceptScore W4290804702C114614502 @default.
- W4290804702 hasConceptScore W4290804702C134306372 @default.
- W4290804702 hasConceptScore W4290804702C14158598 @default.
- W4290804702 hasConceptScore W4290804702C190470478 @default.
- W4290804702 hasConceptScore W4290804702C195065555 @default.
- W4290804702 hasConceptScore W4290804702C202444582 @default.
- W4290804702 hasConceptScore W4290804702C2524010 @default.
- W4290804702 hasConceptScore W4290804702C2777105136 @default.
- W4290804702 hasConceptScore W4290804702C33923547 @default.
- W4290804702 hasConceptScore W4290804702C37914503 @default.
- W4290804702 hasConceptScore W4290804702C9136319 @default.
- W4290804702 hasLocation W42908047021 @default.
- W4290804702 hasOpenAccess W4290804702 @default.
- W4290804702 hasPrimaryLocation W42908047021 @default.
- W4290804702 hasRelatedWork W1981909949 @default.
- W4290804702 hasRelatedWork W1988928836 @default.
- W4290804702 hasRelatedWork W2003788739 @default.
- W4290804702 hasRelatedWork W2012169275 @default.
- W4290804702 hasRelatedWork W2022384357 @default.
- W4290804702 hasRelatedWork W2051622274 @default.
- W4290804702 hasRelatedWork W2529782299 @default.
- W4290804702 hasRelatedWork W2767905351 @default.
- W4290804702 hasRelatedWork W2901496727 @default.
- W4290804702 hasRelatedWork W3105006000 @default.
- W4290804702 isParatext "false" @default.
- W4290804702 isRetracted "false" @default.
- W4290804702 workType "article" @default.