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SOME NEW BONNESEN-STYLE INEQUALITIES

  • Zhou, Jiazu (SCHOOL OF MATHEMATICS AND STATISTICS SOUTHWEST UNIVERSITY) ;
  • Xia, Yunwei (SCHOOL OF MATHEMATICS AND STATISTICS SOUTHWEST UNIVERSITY) ;
  • Zeng, Chunna (SCHOOL OF MATHEMATICS AND STATISTICS SOUTHWEST UNIVERSITY)
  • 투고 : 2009.11.03
  • 발행 : 2011.03.01

초록

By evaluating the containment measure of one domain to contain another, we will derive some new Bonnesen-type inequalities (Theorem 2) via the method of integral geometry. We obtain Ren's sufficient condition for one domain to contain another domain (Theorem 4). We also obtain some new geometric inequalities. Finally we give a simplified proof of the Bottema's result.

과제정보

연구 과제 주관 기관 : CNSF

참고문헌

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피인용 문헌

  1. The Bonnesen isoperimetric inequality in a surface of constant curvature vol.55, pp.9, 2012, https://doi.org/10.1007/s11425-012-4405-z
  2. Reverse Bonnesen style inequalities in a surface $$\mathbb{X}_\varepsilon ^2$$ of constant curvature vol.56, pp.6, 2013, https://doi.org/10.1007/s11425-013-4578-0
  3. Some Bonnesen-style inequalities for higher dimensions vol.28, pp.12, 2012, https://doi.org/10.1007/s10114-012-9657-6
  4. ON THE ISOPERIMETRIC DEFICIT UPPER LIMIT vol.50, pp.1, 2013, https://doi.org/10.4134/BKMS.2013.50.1.175
  5. On containment measure and the mixed isoperimetric inequality vol.2013, pp.1, 2013, https://doi.org/10.1186/1029-242X-2013-540
  6. Bonnesen-style symmetric mixed inequalities vol.2016, pp.1, 2016, https://doi.org/10.1186/s13660-016-1146-5
  7. Bonnesen-style inequalities on surfaces of constant curvature vol.2018, pp.1, 2018, https://doi.org/10.1186/s13660-018-1918-1
  8. Reverse Bonnesen-style inequalities on surfaces of constant curvature vol.29, pp.06, 2018, https://doi.org/10.1142/S0129167X18500404