000069635 001__ 69635 000069635 005__ 20190709135523.0 000069635 0247_ $$2doi$$a10.4171/RMI/968 000069635 0248_ $$2sideral$$a97240 000069635 037__ $$aART-2017-97240 000069635 041__ $$aeng 000069635 100__ $$0(orcid)0000-0003-1256-3671$$aAlonso Gutiérrez, David$$uUniversidad de Zaragoza 000069635 245__ $$aBounding the integral of powered i-th mean curvatures 000069635 260__ $$c2017 000069635 5060_ $$aAccess copy available to the general public$$fUnrestricted 000069635 5203_ $$aWe get estimates for the integrals of powered i-th mean curvatures, 1 = i = n - 1, of compact and convex hypersurfaces, in terms of the quermaßintegrals of the corresponding C 2 + convex bodies. These bounds will be obtained as consequences of a most general result for functions defined on a general probability space. From this result, similar estimates for the integrals of any convex transformation of the elementary symmetric functions of the radii of curvature of C 2 + convex bodies will be also proved, both, in terms of the quermaßintegrals, and of the roots of their Steiner polynomials. Finally, the radial function is considered, and estimates of the corresponding integrals are obtained in terms of the dual quermaßintegrals. 000069635 540__ $$9info:eu-repo/semantics/openAccess$$aAll rights reserved$$uhttp://www.europeana.eu/rights/rr-f/ 000069635 590__ $$a1.039$$b2017 000069635 591__ $$aMATHEMATICS$$b61 / 309 = 0.197$$c2017$$dQ1$$eT1 000069635 592__ $$a1.629$$b2017 000069635 593__ $$aMathematics (miscellaneous)$$c2017$$dQ1 000069635 655_4 $$ainfo:eu-repo/semantics/article$$vinfo:eu-repo/semantics/submittedVersion 000069635 700__ $$aHernández Cifre, María Ángeles 000069635 700__ $$aMartínez Fernández, Antonio Roberto 000069635 7102_ $$12006$$2015$$aUniversidad de Zaragoza$$bDpto. Matemáticas$$cÁrea Análisis Matemático 000069635 773__ $$g33, 4 (2017), 1197-1218$$pRev. mat. iberoam.$$tREVISTA MATEMATICA IBEROAMERICANA$$x0213-2230 000069635 8564_ $$s319494$$uhttps://zaguan.unizar.es/record/69635/files/texto_completo.pdf$$yPreprint 000069635 8564_ $$s58856$$uhttps://zaguan.unizar.es/record/69635/files/texto_completo.jpg?subformat=icon$$xicon$$yPreprint 000069635 909CO $$ooai:zaguan.unizar.es:69635$$particulos$$pdriver 000069635 951__ $$a2019-07-09-11:58:40 000069635 980__ $$aARTICLE