Abstract
Associated with the L p -curvature image defined by Lutwak, some inequalities for extended mixed p-affine surface areas of convex bodies and the support functions of L p -projection bodies are established. As a natural extension of a result due to Lutwak, an L p -type affine isoperimetric inequality, whose special cases are L p -Busemann-Petty centroid inequality and L p -affine projection inequality, respectively, is established. Some L p -mixed volume inequalities involving L p -projection bodies are also established.
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Lv, S., Leng, G. The L p -curvature images of convex bodies and L p -projection bodies. Proc Math Sci 118, 413–424 (2008). https://doi.org/10.1007/s12044-008-0032-6
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DOI: https://doi.org/10.1007/s12044-008-0032-6