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Cutting convex curves

Algebra & Discrete Mathematics

Speaker: Edgardo Roldan, National U. Mexico
Location: 1147 MSB
Start time: Mon, Oct 13 2014, 1:10PM

We show that for any two convex curves C_1 and C_2 in R^d parametrized by [0,1] with opposite orientations, there exists a hyperplane H with the following property: For any t\in [0,1] the points C_1(t) and C_2(t) are never in the same open halfspace bounded by H. We discuss the reasons for this result and its applications in convex geometry.