Speaker
Giovanni Alberti
(Università di Pisa)
Description
In this talk I will consider the following problem of isoperimetric type:
Given a set E in $\mathbb{R}^d$ with finite volume, is it possible to find an hyperplane $P$ that splits $E$ in two parts with equal volume, and such that the area of the cut (that is, the intersection of $P$ and $E$) is of the expected order, namely $(vol(E))^{1-1/d}$?
We can show that the answer is positive if the dimension $d$ is $3$ or higher, but, somewhat surprisingly, our proof breaks down completely in dimension $d=2$, and we do not know what happens in this case.
(However we know that the answer is positive even for $d=2$ if we allow cuts that are not exactly planar, but close to planar.)
This is a work in progress with Alan Chang (Princeton University).
Primary authors
Alan Chang
Giovanni Alberti
(Università di Pisa)
