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Extremal Cubics on the Circle and the 2-sphere

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Abstract

We study balls of homogeneous cubics on \({\mathbb {R}}^n\), \(n = 2,3\), which are bounded by unity on the unit sphere. For \(n = 2\) we completely describe the facial structure of this norm ball, while for \(n = 3\) we classify all extremal points and describe some families of faces.

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Acknowledgements

We would like to thank an anonymous referee for suggestions to improve the paper.

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Authors and Affiliations

  1. LJK, Univ. Grenoble Alpes, CNRS, 38000, Grenoble, France

    Roland Hildebrand & Anastasiia Ivanova

  2. HSE University, 20 Myasnitskaya ulitsa, 101000, Moscow, Russian Federation

    Anastasiia Ivanova

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  1. Roland Hildebrand
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  2. Anastasiia Ivanova
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Correspondence to Anastasiia Ivanova.

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Hildebrand, R., Ivanova, A. Extremal Cubics on the Circle and the 2-sphere. Results Math 77, 135 (2022). https://doi.org/10.1007/s00025-022-01659-8

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