Abstract. The projection body of order one of a convex body K in R^n is the body whose support function is, up to a constant, the average mean width of the orthogonal projections of K onto hyperplanes through the origin. The paper contains an inequality for the support function of the projection body of order one of K which implies in particular that such a function is strictly convex, unless K has dimension one or two. Furthermore, an existence problem related to the reconstruction of a convex body is discussed to highlight the different behavior of the area measures of order one and of order n − 1.
Campi, S., Gronchi, P. (2009). On projection bodies of order one. CANADIAN MATHEMATICAL BULLETIN, 52(3), 349-360 [10.4153/CMB-2009-038-6].
On projection bodies of order one
CAMPI S.;
2009-01-01
Abstract
Abstract. The projection body of order one of a convex body K in R^n is the body whose support function is, up to a constant, the average mean width of the orthogonal projections of K onto hyperplanes through the origin. The paper contains an inequality for the support function of the projection body of order one of K which implies in particular that such a function is strictly convex, unless K has dimension one or two. Furthermore, an existence problem related to the reconstruction of a convex body is discussed to highlight the different behavior of the area measures of order one and of order n − 1.
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https://hdl.handle.net/11365/20440
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