Nonsymmetric extension of the Green–Osher inequality

Abstract

In this paper we obtain the extended Green–Osher inequality when two smooth, planar strictly convex bodies are at a dilation position and show the necessary and sufficient condition for the case of equality.

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Acknowledgements

I am grateful to the anonymous referee for his or her careful reading of the original manuscript of this paper and giving us many invaluable comments. I would also like to thank Professor Shengliang Pan for posing this problem to me.

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Correspondence to Yunlong Yang.

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The author is supported by the Doctoral Scientific Research Foundation of Liaoning Province (No. 20170520382) and the Fundamental Research Funds for the Central Universities (No. 3132017046).

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Yang, Y. Nonsymmetric extension of the Green–Osher inequality. Geom Dedicata 203, 155–161 (2019). https://doi.org/10.1007/s10711-019-00430-8

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Keywords

  • Dilation position
  • Green–Osher’s inequality
  • Nonsymmetric
  • Relative Steiner polynomial

Mathematics Subject Classification 2010

  • 52A40
  • 52A10