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Intersection Bodies in ℝ4

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Abstract:

Intersection bodies were introduced in 1988 by Lutwak, who found a close connection between those bodies and the well-known 1956 Busemann-Petty problem, which asks whether origin symmetric convex bodies with larger central hyperplane sections also have greater volume. The author has recently shown that an origin symmetric star body K is an intersection bodyif and only if the function ‖x‖-1K is a positive definite distribution, where ‖x‖K =min{a>=0: x∈aK}. We use this result to prove that theunit balls of the spaces ℓ4q , 2=5 the unit balls of the spacesℓnq , 2

Document Type: Research Article

Affiliations: Division of Mathematics and Statistics, University of Texas at San Antonio, San Antonio, Texas, 78249

Publication date: June 1, 1998

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