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.
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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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Research of the authors is supported by NSFC No.11871373 and the China Postdoctoral Science Foundation No.2019M651330.
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Hu, J., Xiong, G. & Zou, D. Affine isoperimetric inequalities for intersection mean ellipsoids. Calc. Var. 58, 191 (2019). https://doi.org/10.1007/s00526-019-1643-8
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DOI: https://doi.org/10.1007/s00526-019-1643-8