Abstract
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 .
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