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Affine isoperimetric inequalities for intersection mean ellipsoids

  • Jiaqi Hu
  • Ge XiongEmail author
  • Du Zou
Article
  • 81 Downloads

Abstract

A variational formula for Lutwak’s dual affine quermassintegrals \({\widetilde{\Lambda }}_{j}\) of convex bodies in \({\mathbb {R}}^n\) is established when \(1\le j\le n-1.\) Using new ellipsoids associated with the intersection functions of convex bodies, we prove several sharp affine isoperimetric inequalities.

Mathematics Subject Classification

52A40 

Notes

Acknowledgements

Part of this work was done when we were visiting Chern Institute of Mathematics in 2017. We would like to thank Professors Zhang Weiping and Feng Huitao and the institute for their hospitality and financial support. We are grateful to the referee for many suggested improvements and for the thoughtful and careful reading given to the original draft of this paper.

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Copyright information

© Springer-Verlag GmbH Germany, part of Springer Nature 2019

Authors and Affiliations

  1. 1.School of Mathematical SciencesFudan UniversityShanghaiPeople’s Republic of China
  2. 2.School of Mathematical SciencesTongji UniversityShanghaiPeople’s Republic of China
  3. 3.Department of MathematicsWuhan University of Science and TechnologyWuhanPeople’s Republic of China

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