Breakthrough in Conformal Mapping

Few analytical techniques are better known to students of applied mathematics than conformal mapping. It is the classical method for solving problems in continuum mechanics, electrostatics, and other fields involving the two-dimensional Laplace and Poisson equations. To employ the method, one needs an explicit mapping function from some standard domain— such as the unit disk or upper half plane—to the region of interest. For a broad class of simply connected domains, and a few doubly connected ones, the Schwarz–Christoffel (SC) formula provides the required map. But until quite recently, there was no analogue of the SC formula for multiply connected domains. Today, however, the “connectivity barrier” has been breached in at least two places.