A characterization of all loglinear inequalities for three quermassintegrals of convex bodies
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- by Peter Gritzmann PDF
- Proc. Amer. Math. Soc. 104 (1988), 563-570 Request permission
Abstract:
We give a complete characterization of all inequalities of the type $W_i^\alpha (K)W_j^\beta (K)W_k^\gamma (K) \geq c$, where $K$ is an arbitrary convex body of Euclidean $d$-space, ${W_l}(K),l = i,j,k$, denotes the $l$th quermassintegral of $K$ and $\alpha ,\beta ,\gamma$ and $c$ are arbitrary reals. A special case of such inequalities is the classical isoperimetric inequality for the volume and surface area of convex bodies. It turns out that all nontrivial inequalities of this type can be generated by means of $d - 1$ basic inequalities, the Fenchel-Alexandrov inequalities.References
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Additional Information
- © Copyright 1988 American Mathematical Society
- Journal: Proc. Amer. Math. Soc. 104 (1988), 563-570
- MSC: Primary 52A40
- DOI: https://doi.org/10.1090/S0002-9939-1988-0962829-5
- MathSciNet review: 962829