The L
p
-curvature images of convex bodies and L
p
-projection bodies |
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| Authors: | Songjun Lv Gangsong Leng |
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| Institution: | (1) College of Mathematics and Computer Science, Chongqing Normal University, Chongqing, 400047, People’s Republic of China;(2) Department of Mathematics, Shanghai University, Shanghai, 200444, People’s Republic of China |
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| 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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| Keywords: | p-Curvature image p-affine surface area L p -projection body L p -mixed volume L p -dual mixed volume |
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