# Bonnesen-Style Isoperimetric Inequalities

by Robert Osserman

Year of Award: 1980

Publication Information: The American Mathematical Monthly, vol. 86, 1979, pp. 1-29

Summary: The author considers generalizations of the isoperimetric inequality of the form $$L^2 - 4 \pi A \geq B$$, where $$C$$ is a simple closed curve of length $$L$$ in the plane, $$A$$ is the area enclosed by $$C$$ and $$B$$ is non-negative, can vanish only when $$C$$ is a circle, and has geometric significance.