2026-06-30T01:23:07Zhttps://docta.ucm.es/rest/oai/requestoai:docta.ucm.es:20.500.14352/243652024-07-12T16:25:37Zcom_20.500.14352_14col_20.500.14352_15
Docta Complutense
author
Villanueva Díez, Ignacio
2023-06-18T06:50:24Z
2023-06-18T06:50:24Z
2016
Villanueva Díez, I. «Radial Continuous Rotation Invariant Valuations on Star Bodies». Advances in Mathematics, vol. 291, marzo de 2016, pp. 961-81. DOI.org (Crossref), https://doi.org/10.1016/j.aim.2015.12.030.
0001-8708
10.1016/j.aim.2015.12.030
https://hdl.handle.net/20.500.14352/24365
https//doi.org/10.1016/j.aim.2015.12.030
http://www.sciencedirect.com/science/article/pii/S0001870816000335http://arxiv.org/abs/1503.06064
We characterize the positive radial continuous and rotation invariant valuations V defined on the star bodies of Rn as the applications on star bodies which admit an integral representation with respect to the Lebesgue measure. That is,V(K)=∫Sn−1θ(ρK)dm, where θ is a positive continuous function, ρK is the radial function associated to K and m is the Lebesgue measure on Sn−1. As a corollary, we obtain that every such valuation can be uniformly approximated on bounded sets by a linear combination of dual quermassintegrals.
eng
Radial continuous rotation invariant valuations on star bodies
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