A survey of applications of the Julia variation (Q2769232)

This is an excellent survey of the uses of the Julia variation and its modifications by Krzyż and others in the field of geometric function theory. The first two authors have been quite active in the development of the use of these methods. This survey is well written, authoritative, and well worth close study by anyone wishing to work in this area. The Julia variation was developed as an application of the Hadamard variation of the Green's function to the mapping function of a domain with a smooth boundary. Warshawski and later Bernard (independently) proved that the boundary could be piecewise smooth with ``corners''. This allowed Bernard and Pierce along with others to develop powerful methods using the approximation of extremal domains by sequences of simpler domains. These ideas are well demonstrated here.