J. Korean Math. Soc. 2007; 44(6): 1363-1372
Printed November 1, 2007
Copyright © The Korean Mathematical Society.
Jiazu Zhou and Fangwei Chen
Southwest University, Wuhan University
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.
MSC numbers: Primary 52A22, 53C65; Secondary 51C16
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