All Questions

Recall that a plane continuum is a closed, bounded, connected subset of the plane. It is non-degenerate if it contains at least two points. (We may sometimes just say "continuum" even if we ...

The Kakeya needle problem asks for the minimum area planar region in which one can completely turn around a line segment through a series of translations and rotations. There is no minimum: There are &...

Fix a real number $0\leq t\leq 1$ and an integer $n>1$. Let $\mathbb{S}^{n-1}\subset\mathbb{R}^n$ denote the unit hypersphere. Define $$d_N(n;t):=\max\sum_{i<j}\Vert P_i-P_j\Vert_2^t$$ where ...

Given a set $S$, a function $M: S\times S \rightarrow S$ is a mean if it satisfies the properties: $M(a,a)=a\qquad$ (identity) $M(a,b)=M(b,a)\qquad$ (commutativity). and possibly $M(M(a,b),M(a,c))=...