Geodesic
Inequalities for the Surface Area of Projections of Convex Bodies
Canadian journal of mathematics, Tome 70 (2018) no. 4, pp. 804-823

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DOI

We provide general inequalities that compare the surface area $S(K)$ of a convex body $K$ in ${{\mathbb{R}}^{n}}$ to the minimal, average, or maximal surface area of its hyperplane or lower dimensional projections. We discuss the same questions for all the quermassintegrals of $K$ . We examine separately the dependence of the constants on the dimension in the case where $K$ is in some of the classical positions or $K$ is a projection body. Our results are in the spirit of the hyperplane problem, with sections replaced by projections and volume by surface area.
DOI : 10.4153/CJM-2016-051-x
Mots-clés : 52A20, 46B05, surface area, convex body, projection 
Giannopoulos, Apostolos; Koldobsky, Alexander; Valettas, Petros. Inequalities for the Surface Area of Projections of Convex Bodies. Canadian journal of mathematics, Tome 70 (2018) no. 4, pp. 804-823. doi: 10.4153/CJM-2016-051-x
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     title = {Inequalities for the {Surface} {Area} of {Projections} of {Convex} {Bodies}},
     journal = {Canadian journal of mathematics},
     pages = {804--823},
     year = {2018},
     volume = {70},
     number = {4},
     doi = {10.4153/CJM-2016-051-x},
     url = {http://geodesic.mathdoc.fr/articles/10.4153/CJM-2016-051-x/}
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