Linearity of the volume. Looking for a characterization of sausages

Saorín Gómez, Eugenia; Yepes Nicolás, Jesús

Publication:
Linearity of the volume. Looking for a characterization of sausages

dc.contributor.author	Saorín Gómez, Eugenia
dc.contributor.author	Yepes Nicolás, Jesús
dc.contributor.department	Matemáticas
dc.contributor.other	Facultad de Matemáticas
dc.date.accessioned	2026-02-24T16:24:42Z
dc.date.available	2026-02-24T16:24:42Z
dc.date.copyright	© 2014 Elsevier Inc. All rights reserved.
dc.date.issued	2014-07-30
dc.description.abstract	Let K,E,L be convex bodies, dim⁡L≤1 and K=L+E, a sausage. In this case vol(λK+(1−λ)E)=λvol(K)+(1−λ)vol(E). We prove that under the sole assumption that K and E have an equal volume projection (or a common maximal volume section), if the above equality holds for just one value in (0,1), then K=L+E with dim⁡L≤1. However, even having equality for all λ∈[0,1], if no extra assumption on K,E is done, such a characterization is not possible. This problem is connected with a conjecture relating the roots of the Steiner polynomial of a pair of convex bodies to their relative inradius. Counterexamples for the general case are explicitly given. In the same line, a counterexample to a conjecture by Matheron on inner parallel bodies is also shown.
dc.format	application/pdf
dc.format.extent	22
dc.identifier.citation	Journal of Mathematical Analysis and Applications, Volume 421, Issue 2, 2015, Pages 1081-1100, ISSN 0022-247X, https://doi.org/10.1016/j.jmaa.2014.07.060.
dc.identifier.doi	https://doi.org/10.1016/j.jmaa.2014.07.060
dc.identifier.eissn	1096-0813
dc.identifier.issn	0022-247X
dc.identifier.uri	http://hdl.handle.net/10201/212441
dc.language	eng
dc.publisher	Elsevier
dc.relation	First author is supported by Dirección General de Investigación MTM2011-25377 MCIT and FEDER. Second author is supported by MINECO project MTM2012-34037. Both of them are also supported by “Programa de Ayudas a Grupos de Excelencia de la Región de Murcia”, Fundación Séneca, 04540/GERM/06.
dc.relation.publisherversion	https://www.sciencedirect.com/science/article/pii/S0022247X14007033?via%3Dihub
dc.rights	Attribution-NonCommercial-NoDerivatives 4.0 International	*
dc.rights.accessRights	info:eu-repo/semantics/openAccess
dc.rights.uri	http://creativecommons.org/licenses/by-nc-nd/4.0/	*
dc.subject	Linearity of volume
dc.subject	Sausages
dc.subject	Brunn–Minkowski inequality
dc.subject	Roots of Steiner polynomial
dc.subject	Inner parallel body
dc.subject	Linearity of determinant
dc.subject.ods	No relacionado con ningún objetivo de desarrollo sostenible
dc.title	Linearity of the volume. Looking for a characterization of sausages
dc.type	info:eu-repo/semantics/article
dc.type.version	info:eu-repo/semantics/acceptedVersion
dspace.entity.type	Publication	es
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