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Bonnesen-Style Isoperimetric Inequalities

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.

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About the Author: (from The American Mathematical Monthly, vol. 86 (1979)) Robert Osserman received his Ph.D. from Harvard under the supervision of L. Ahlfors. Since then he has been on the faculty of Stanford University, with temporary or visiting positions at the University of Colorado, New York University, Harvard, and the University of Warwick. During 1960-61 he was Head of the Mathematics Branch of the Office of Naval Research; he was a Fulbright Lecturer at the University of Paris (Orsay) in 1965-66 and held a Guggenheim Fellowship in 1976-77.

 

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Robert Osserman
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Robert Osserman
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Wednesday, September 24, 2008
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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.

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