
> 
> Given $nD$ finite measures $µ\_1, . . ., µ\_{nD}$ in $\mathbb{R}^n$
>  does there exists a set of at most D hyperplanes that bisect each of the measures? 
> 
> 
> 


How far is this problem explained?


That is closely related to a conjecture in *L. Barba and P. Schnider, Sharing a pizza: bisecting masses with two cuts, Proceedings of the 29th Canadian
Conference on Computational Geometry, CCCG’17*.


Definition: A Hyperplane bisects $\mu$ iff the value of $\mu$ on two sides of the hyperplane are equal.



A conjecture: Given $nD$ finite measures that bisects
The [7-day-old paper](https://arxiv.org/abs/1803.02842) by Alfredo Hubard answers this question positively.


*Update on 16 May*: The paper has been revised. It is now coauthored with Roman Karasev and claims to treat only the case when the dimension is of the form $2^t$.


