Cross  -sections of star bodies and dual mixed volumes |
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| Authors: | Songjun Lv Gangsong Leng |
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| Affiliation: | Department of Mathematics, Shanghai University, Shanghai, People's Republic of China 200444 ; Department of Mathematics, Shanghai University, Shanghai, People's Republic of China 200444 |
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| Abstract: | In this paper, we establish an extension of Funk's section theorem. Our result has the following corollary: If  is a star body in  whose central  -slices have the same volume (with appropriate dimension) as the central  -slices of a centered body  , then the dual quermassintegrals satisfy  , for any  , with equality if and only if  . The case that  is a centered body implies Funk's section theorem. |
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| Keywords: | Star body cross $i$-section dual mixed volume Radon transform |
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