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Brannen's Conjecture

Brannen's conjecture proposes that simplices maximize the normalized volume of the projection body among convex bodies in each dimension n>=2. Writing R_n(K)=vol_n(PiK)/vol_n(K)^(n-1), the simplex value and proposed upper bound are

R_n(K)<=c_n=((n+1)n^n)/(n!).

See also

Convex Body, Petty's Projection-Volume Conjecture, Projection Body, Simplex

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References

Brannen, N. S. "Volumes of Projection Bodies." Mathematika 43, 255-264, 1996. https://doi.org/10.1112/S002557930001175X.Saroglou, C. and Zvavitch, A. "Iterations of the Projection Body Operator and a Remark on Petty's Conjectured Projection Inequality." J. Funct. Anal. 272, 613-630, 2017. https://doi.org/10.1016/j.jfa.2016.08.015.

Cite this as:

Weisstein, Eric W. "Brannen's Conjecture." From MathWorld--A Wolfram Resource. https://mathworld.wolfram.com/BrannensConjecture.html

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