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# Convex Forms That Are Not Sums of Squares

@inproceedings{BlekhermanConvexFT, title={Convex Forms That Are Not Sums of Squares}, author={Grigoriy Blekherman} }

An orbitope is the convex hull of an orbit of a point under the action of a compact group. We derive bounds on volumes of sections of polar bodies of orbitopes, extending methods developed in [BB03]. As an application we realize the cone of convex forms as a section of the cone of nonnegative bi-homogeneous forms and estimate its volume. A convex form has to be nonnegative, but it has not been previously shown that there exist convex forms that are not sums of squares. Combining with the bounds… CONTINUE READING