Abstract
For convex bodiesD inR n it is shown that the isoperimetric deficit ofD is minorized by a constant times the square of thebarycentric asymmetry β(D) ofD. Here β(D) is defined as the volume ofD∖B D divided by the volume ofD, whereB D denotes the ball centred at the barycentre ofD and having the same volume asD.
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Dedicated to the memory of Børge Jessen
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Fuglede, B. Lower estimate of the isoperimetric deficit of convex domains inR n in terms of asymmetry. Geom Dedicata 47, 41–48 (1993). https://doi.org/10.1007/BF01263492
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DOI: https://doi.org/10.1007/BF01263492