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Affine Isoperimetric Inequalities for L p Geominimal Surface Area

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Real and Complex Submanifolds

Part of the book series: Springer Proceedings in Mathematics & Statistics ((PROMS,volume 106))

Abstract

We present some L p affine isoperimetric inequalities for L p geominimal surface area. In particular, we obtain an analogue of Blaschke-Santaló inequality. We give an integral formula of L p geominimal surface area by the p-Petty body. Furthermore, we introduce the concept of L p mixed geominimal surface area which is a nature extension of L p geominimal surface area. We also extend Lutwak’s results for L p mixed geominimal surface area.

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Acknowledgements

This research is supported in part by the Doctor Starting Foundation of Hubei University for Nationalities (No. MY2014B001) and National Natural Science Foundation of China (No. 11271302).

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Authors and Affiliations

  1. Department of Mathematics, Hubei University for Nationalities, Enshi, Huibei, 445000, China

    Baocheng Zhu

  2. College of Mathematical Science, Kaili University, Kaili, Guizhou, 556000, China

    Jiazu Zhou

  3. School of Mathematics and Statistics, Southwest University, Chongqing, 400715, China

    Baocheng Zhu, Jiazu Zhou & Wenxue Xu

Authors
  1. Baocheng Zhu
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  2. Jiazu Zhou
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  3. Wenxue Xu
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Corresponding author

Correspondence to Baocheng Zhu .

Editor information

Editors and Affiliations

  1. Department of Mathematics, Kyungpook National University, Daegu, Republic of Korea

    Young Jin Suh

  2. Department of Mathematics, King’s College London, London, UK

    Jürgen Berndt

  3. Department of Mathematics, Osaka City University, Osaka, Japan

    Yoshihiro Ohnita

  4. Department of Applied Mathematics, Kyung Hee University, Yongin, Republic of Korea

    Byung Hak Kim

  5. The Center for Geometry and its Applications, Pohang University of Science and Technology, Pohang, Republic of Korea

    Hyunjin Lee

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Zhu, B., Zhou, J., Xu, W. (2014). Affine Isoperimetric Inequalities for L p Geominimal Surface Area. In: Suh, Y.J., Berndt, J., Ohnita, Y., Kim, B.H., Lee, H. (eds) Real and Complex Submanifolds. Springer Proceedings in Mathematics & Statistics, vol 106. Springer, Tokyo. https://doi.org/10.1007/978-4-431-55215-4_15

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