Abstract
Let \(K_i\) be plane convex bodies with the perimeters \(L_{K_i}\) and areas \(A_{K_i}\) for \(i=1,2\), respectively. In this paper, the lower bounds of the mixed isoperimetric deficit \(\Delta _{K_1,K_2}=L_{K_1}^2L_{K_2}^2-16\pi ^2 A_{K_1}A_{K_2}\) are obtained; these bounds involve the areas enclosed by the evolute and the Wigner caustic, Hausdorff and \(L_2\) distances between two convex bodies.
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Communicated by Rosihan M. Ali.
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This work was supported by the Natural Science Foundation of Anhui Province (No. 1908085MA05) and University Natural Science Research Project of Anhui Province (No. KJ2019A0590) and Excellent Young Talents Fund Program of Higher Education Institutions of Anhui Province (gxyqZD2020022).
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Zhang, D. The Lower Bounds of the Mixed Isoperimetric Deficit. Bull. Malays. Math. Sci. Soc. 44, 2863–2872 (2021). https://doi.org/10.1007/s40840-020-01067-7
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DOI: https://doi.org/10.1007/s40840-020-01067-7