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On Blaschke-Minkowski homomorphisms

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Abstract

In this article we establish a Brunn-Minkowski-type inequality for mixed Blaschke-Minkowski homomorphisms.

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References

  1. Aleksandrov A.D.: On the theory of mixed volumes of convex bodies, II: new inequalities between mixed volumes and their applications. Mat. Sb. 2, 1205–1238 (1937) (Russian)

    MATH  Google Scholar 

  2. Haberl C., Schuster F.E.: General L p affine isoperimetric inequalities. J. Differ. Geom. 83, 1–26 (2009)

    MATH  MathSciNet  Google Scholar 

  3. Kiderlen M.: Blaschke- and Minkowski-Endomorphisms of convex bodies. Trans. Am. Math. Soc. 35, 5539–5564 (2006)

    Article  MathSciNet  Google Scholar 

  4. Ludwig M.: Minkowski valuations. Trans. Am. Math. Soc. 357(10), 4191–4213 (2005)

    Article  MATH  MathSciNet  Google Scholar 

  5. Lutwak E.: Mixed projection inequalities. Trans. Am. Math. Soc. 287(1), 91–105 (1985)

    MATH  MathSciNet  Google Scholar 

  6. Lutwak E.: Volume of mixed bodies. Trans. Am. Math. Soc. 294(2), 487–500 (1986)

    MATH  MathSciNet  Google Scholar 

  7. Lutwak E.: Inequalities for mixed projection bodies. Trans. Am. Math. Soc. 339, 901–916 (1993)

    Article  MATH  MathSciNet  Google Scholar 

  8. Schneider, R., Schuster, F.E.: Rotation equivariant Minkowski valuations. Int. Math. Res. Not., Art. ID 72894, p. 20 (2006)

  9. Schuster F.E.: Convolutions and multiplier transformations of convex bodies. Trans. Am. Math. Soc. 359, 5567–5591 (2007)

    Article  MATH  MathSciNet  Google Scholar 

  10. Schuster F.E.: Volume inequalities and additive maps of convex bodies. Mathematika 53, 211–234 (2006)

    Article  MATH  MathSciNet  Google Scholar 

  11. Schuster F.E.: Valuations and Busemann-Petty type problems. Adv. Math. 219, 344–368 (2008)

    Article  MATH  MathSciNet  Google Scholar 

  12. Schuster, F.E.: Crofton measures and Minkowski valuations. Duke Math. J. (in press)

  13. Zhao C.J., Leng G.S.: Brunn-Mibkowski inequality for mixed intersection bodies. J. Math. Anal. Appl. 301, 115–123 (2005)

    Article  MATH  MathSciNet  Google Scholar 

  14. Zhao C.J.: On intersection and mixed intersection bodies. Geom. Dedicata 141, 109–122 (2009)

    Article  MATH  MathSciNet  Google Scholar 

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Authors and Affiliations

  1. Department of Mathematics, China Jiliang University, 310018, Hangzhou, People’s Republic of China

    Chang-jian Zhao

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  1. Chang-jian Zhao
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Correspondence to Chang-jian Zhao.

Additional information

Research is supported by National Natural Science Foundation of China (10971205).

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Zhao, Cj. On Blaschke-Minkowski homomorphisms. Geom Dedicata 149, 373–378 (2010). https://doi.org/10.1007/s10711-010-9487-6

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  • DOI: https://doi.org/10.1007/s10711-010-9487-6

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