I'm speaking in reference to Hadwiger's conjecture in combinatorial geometry "Can every $n$-dimensional convex body be covered by $2^{n}$ smaller copies of itself?"
I am aware that some upper bounds greater than $2^n$ already exist, and I was wondering whether an analogue for this problem exists that also takes concave n-dimensional bodies into account, and whether upper bounds exist for these? Or does allowing concavity cause other problems that lead to it being impossible to provide any sort of upper bound?
Kind Regards, V