Bonnesen-type inequalities for surfaces of constant curvature

A Bonnesen-type inequality is a sharp isoperimetric inequality that includes an error estimate in terms of inscribed and circumscribed regions. A kinematic technique is used to prove a Bonnesen-type inequality for the Euclidean sphere (having constant Gauss curvature κ>0) and the hyperbolic plane (having constant Gauss curvature κ<0). These generalized inequalities each converge to the classical Bonnesen-type inequality for the Euclidean plane as κ→0.