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THE BONNESEN-TYPE INEQUALITIES IN A PLANE OF CONSTANT CURVATURE

  • Zhou, Jiazu ;
  • Chen, Fangwei
  • Published : 2007.11.30

Abstract

We investigate the containment measure of one domain to contain in another domain in a plane $X^{\kappa}$ of constant curvature. We obtain some Bonnesen-type inequalities involving the area, length, radius of the inscribed and the circumscribed disc of a domain D in $X^{\kappa}$.

Keywords

isoperimetric inequality;Bonessen inequality;kinematic measure;containment measure;hyperbolic plane;projective plane;geodesic disc

References

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  3. An isoperimetric deficit upper bound of the convex domain in a surface of constant curvature vol.53, pp.8, 2010, https://doi.org/10.1007/s11425-010-4018-3
  4. ON THE ISOPERIMETRIC DEFICIT UPPER LIMIT vol.50, pp.1, 2013, https://doi.org/10.4134/BKMS.2013.50.1.175
  5. Some Bonnesen-style inequalities for higher dimensions vol.28, pp.12, 2012, https://doi.org/10.1007/s10114-012-9657-6
  6. Translative containment measure and symmetric mixed isohomothetic inequalities vol.58, pp.12, 2015, https://doi.org/10.1007/s11425-015-5074-5
  7. A kinematic formula for integral invariant of degree 4 in real space form vol.30, pp.8, 2014, https://doi.org/10.1007/s10114-014-1266-0
  8. Bonnesen-style inequality for the first eigenvalue on a complete surface of constant curvature vol.2017, pp.1, 2017, https://doi.org/10.1186/s13660-017-1462-4
  9. SOME NEW BONNESEN-STYLE INEQUALITIES vol.48, pp.2, 2011, https://doi.org/10.4134/JKMS.2011.48.2.421
  10. Bonnesen-style inequalities on surfaces of constant curvature vol.2018, pp.1, 2018, https://doi.org/10.1186/s13660-018-1918-1
  11. Reverse Bonnesen-style inequalities on surfaces of constant curvature vol.29, pp.06, 2018, https://doi.org/10.1142/S0129167X18500404