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math.MG2010★ 7 cited
Dvoretzky type theorems for multivariate polynomials and sections of convex bodies
V. L. Dol'nikov, R. N. Karasev
In this paper we prove the Gromov--Milman conjecture (the Dvoretzky type theorem) for homogeneous polynomials on , and improve bounds on the number in the ana…
math.MG2010★ 3 cited
A measure of non-convexity in the plane and the Minkowski sum
R. N. Karasev
In this paper a measure of non-convexity for a simple polygonal region in the plane is introduced. It is proved that for "not far from convex" regions this measure does not decreas…