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Journal of Inequalities and Applications 
Volume 5 (2000), Issue 2, Pages 97-102
doi:10.1155/S1025583400000072

An optimal relative isoperimetric inequality in concave cylindrical domains in ℝn

Inho Kim

Department of Mathematics, Seoul National University, San 56-1, Shinlim-Dong, Kwanack-gu, Seoul 151-742, Korea

Received 2 February 1999; Revised 25 March 1999

Abstract

We prove an optimal relative isoperimetric inequality in concave cylindrical domains in ℝn, which generalizes the well-known two-dimensional relative isoperimetric inequality L2≥2πA in a planar sector with angle greater than or equal to π.