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L p Radial Blaschke-Minkowski Homomorphisms and L p Dual Affine Surface Areas

Author

Listed:
  • Zhonghuan Shen

    (Department of Mathematics, China Three Gorges University, Yichang 443002, China
    Three Gorges Mathematical Research Center, China Three Gorges University, Yichang 443002, China)

  • Weidong Wang

    (Department of Mathematics, China Three Gorges University, Yichang 443002, China
    Three Gorges Mathematical Research Center, China Three Gorges University, Yichang 443002, China)

Abstract

Schuster introduced the notion of radial Blaschke-Minkowski homomorphism and considered the Busemann-Petty problem for volume forms. Whereafter, Wang, Liu and He presented the L p radial Blaschke-Minkowski homomorphisms and extended Schuster’s results. In this paper, associated with L p dual affine surface areas, we give an affirmative and a negative form of the Busemann-Petty problem and establish two Brunn-Minkowski inequalities for the L p radial Blaschke-Minkowski homomorphisms.

Suggested Citation

  • Zhonghuan Shen & Weidong Wang, 2019. "L p Radial Blaschke-Minkowski Homomorphisms and L p Dual Affine Surface Areas," Mathematics, MDPI, vol. 7(4), pages 1-14, April.
    • Handle: RePEc:gam:jmathe:v:7:y:2019:i:4:p:343-:d:221627
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