Analysis & Applied Math

Given a finite subset $E \subset \mathbb{C}$, Chebotarev’s continuum problem consists in finding a continuum $K \subset \mathbb{C}$ of minimal logarithmic capacity that contains $E$. In this talk we will discuss a modification of Chebotarev’s problem, where $E$ and $K$ are subsets of $\mathbb{C}^+$ and where we minimize the Dirichlet energy of $\mathbb{C}^+ \setminus K$ instead of the logarithmic capacity of $K$. The later problem was motivated by study of focusing NLS soliton condensates of minimal intensity with prescribed endpoints of the spectral support set.