Open Access
November 2014 Centroid bodies and the convexity of area functionals
Andreas Bernig
J. Differential Geom. 98(3): 357-373 (November 2014). DOI: 10.4310/jdg/1406552275


We introduce a new volume definition on normed vector spaces. We show that the induced $k$-area functionals are convex for all $k$. In the particular case $k = 2$, our theorem implies that Busemann’s 2-volume density is convex, which was recently shown by Burago-Ivanov. We also show how the new volume definition is related to the centroid body and prove some affine isoperimetric inequalities.


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Andreas Bernig. "Centroid bodies and the convexity of area functionals." J. Differential Geom. 98 (3) 357 - 373, November 2014.


Published: November 2014
First available in Project Euclid: 28 July 2014

zbMATH: 1302.52007
MathSciNet: MR3238312
Digital Object Identifier: 10.4310/jdg/1406552275

Rights: Copyright © 2014 Lehigh University

Vol.98 • No. 3 • November 2014
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