Convex equipartitions of convex sets

Alfredo Hubard

Department of Mathematics, New York University, New York, USA

Department of Mathematics, New York University, New York, USA

2012/2/15 Wed 4PM-5PM

Imagine that you are cooking chicken at a party. You will cut the raw chicken fillet with a sharp knife, marinate each of the pieces in a spicy sauce and then fry the pieces. The surface of each piece will be crispy and spicy. Can you cut the chicken so that all your guests get the same amount of crispy crust and the same amount of chicken?

We show that if the number of guests is a prime power, n=p

Our proof uses optimal transport and equivariant topology.

We show that if the number of guests is a prime power, n=p

^{k}. Then such partition is possible. We derive this from a more general statement about equipartitions of convex bodies with respect to a measure and d-1 continuous functionals on the space of convex bodies, where d is the dimension the convex body sits in.Our proof uses optimal transport and equivariant topology.

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