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, 349-360.

On projection bodies of order one

CAMPI, STEFANO;
2009

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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Utilizza questo identificativo per citare o creare un link a questo documento: http://hdl.handle.net/11365/20440
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