Abstract
The Busemann theorem states that the intersection body of an origin-symmetric convex body is also convex. In this paper, we prove a version of the Busemann theorem for complex p-convex bodies. Namely that the complex intersection body of an origin-symmetric complex p-convex body is γ-convex for certain γ. The result is the complex analogue of the work of Kim, Yaskin, and Zvavitch on (real) p-convex bodies. Furthermore, we show that the generalized radial qth mean body of a p-convex body is γ-convex for certain γ.
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The authors would like to acknowledge the support from the National Natural Science Foundation of China (11071156), Shanghai Leading Academic Discipline Project (J50101).
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Huang, Q., He, B. & Wang, G. The Busemann theorem for complex p-convex bodies. Arch. Math. 99, 289–299 (2012). https://doi.org/10.1007/s00013-012-0422-y
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DOI: https://doi.org/10.1007/s00013-012-0422-y