Higher dimensional Lemniscates: the geometry of $r$ particles in $n$-space with logarithmic potentials

Ingrid Bauer, Fabrizio Catanese, Antonio Jose Di Scala

We prove some basic theorems concerning lemniscate configurations in an Euclidean space of dimension $n\ge 3$. Lemniscates are defined as follows. Given m points $w_j$ in $\mat…