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Consequences and Extensions of the Brunn-Minkowski Theorem

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New Trends in Geometric Analysis

Part of the book series: RSME Springer Series ((RSME,volume 10))

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Abstract

In this work we study some extensions and consequences of the fundamental Brunn-Minkowski inequality, using two different approaches: on one hand we deal with the so-called Grünbaum inequality, a beautiful consequence of the Brunn-Minkowski theorem which asserts, roughly speaking, that any hyperplane passing through the centroid divides any compact convex set into two not too small parts; on the other hand we study discrete versions of the Brunn-Minkowski inequality for the lattice point enumerator, that is, the functional counting how many points with integer coordinates are contained in a bounded set.

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Acknowledgements

This research is part of the grant PID2021-124157NB-I00, funded by MCIN/ AEI/10.13039/501100011033/ “ERDF A way of making Europe.” It is also supported by “Ayudas a proyectos para el desarrollo de investigación científica y técnica por grupos competitivos,” included in the Programa Regional de Fomento de la Investigación Científica y Técnica (Plan de Actuación 2022) of the Fundación Séneca-Agencia de Ciencia y Tecnología de la Región de Murcia, REF. 21899/PI/22.

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Authors and Affiliations

  1. Dpto. de Matemáticas, Universidad de Murcia, Murcia, Spain

    María A. Hernández Cifre, Eduardo Lucas, Francisco Marín Sola & Jesús Yepes Nicolás

Authors
  1. María A. Hernández Cifre
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  2. Eduardo Lucas
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  3. Francisco Marín Sola
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  4. Jesús Yepes Nicolás
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Corresponding author

Correspondence to Jesús Yepes Nicolás .

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Editors and Affiliations

  1. Departamento de Geometría y Topología, Universidad de Granada, Granada, Spain

    Antonio Alarcón

  2. Departament de Matemàtiques, Universitat Jaume I, Castellón, Spain

    Vicente Palmer

  3. Departamento de Geometría y Topología, Universidad de Granada, Granada, Spain

    César Rosales

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Cifre, M.A.H., Lucas, E., Sola, F.M., Nicolás, J.Y. (2023). Consequences and Extensions of the Brunn-Minkowski Theorem. In: Alarcón, A., Palmer, V., Rosales, C. (eds) New Trends in Geometric Analysis. RSME Springer Series, vol 10. Springer, Cham. https://doi.org/10.1007/978-3-031-39916-9_9

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