Positive harmonic functions in union of chambers
  We characterize the set of positive harmonic functions with Dirichlet boundary conditions in unbounded domains which are union of several different chambers. We analyze the asymptotic behavior of the solutions in connection with the changes in the domain's geometry. Finally we classify all (possibly sign-changing) infinite energy solutions having minimal frequency at the infinite ends of the domain. 
Laura Abatangelo, Susanna Terracini
math.AP