Spatial segregation occurs in population dynamics when k species interact in a highly competitive way. As a model for the study of this phenomenon, we consider the competition-diffusion system of k differential equations x/; i D 1; : : : ; k in a domain D with appropriate boundary conditions. Any u i represents a population density and the parameter determines the interaction strength between the populations. The purpose of this paper is to study the geometry of the limiting configuration as !

more »

... 1 on a planar domain for any number of species. If k is even we show that some limiting configurations are strictly connected to the solution of a Dirichlet problem for the Laplace equation.