A lower bound on critical points of the electric potential of a knot

Max Lipton

Given a knot $K$ parametrized by $r:[0,2\pi ]\to {\mathbb{R}}^3$, we can define the electric potential on its complement by $\Phi (x)={\int }_0^{2\pi }\frac{|r^{\prime }(t)|}{|x-r(t)|}dt$. Physicis…