Shephard's Problem

Measurements of a centered convex body in Euclidean -space (for ) show that its brightness function (thevolume of each projection) is smaller than that of another such body. Is it true that its Volume is also smaller? C. M. Petty and R. Schneider showed in 1967 that the answer is yes if the body with the larger brightness function is aprojection body, but no in general for every .

References

Gardner, R. J. ``Geometric Tomography.'' Not. Amer. Math. Soc. 42, 422-429, 1995.

• Stewart's Theorem
• Stickelberger Relation
• Stick Number
• Stiefel Manifold
• Stiefel-Whitney Class
• Stiefel-Whitney Number
• Stieltjes Constants
• Stieltjes Integral
• Stieltjes' Theorem
• Stieltjes-Wigert Polynomial
• Stirling Cycle Number
• Stirling Number of the First Kind
• Stirling Number of the Second Kind
• Stirling's Approximation
• Stirling Set Number
• Stirling's Finite Difference Formula
• Stirling's Formula
• Stirling's Series
• Stirrup Curve
• Stochastic
• Stochastic Calculus of Variations
• Stochastic Group
• Stochastic Matrix
• Stochastic Process
• Stochastic Resonance