Functionals of Finite Riemann Surfaces

This advanced monograph on finite Riemann surfaces, based on the authors' 1949–50 lectures at Princeton University, remains a fundamental book for graduate students. The Bulletin of the American Mathematical Society hailed the self-contained treatment as the source of "a plethora of ideas, each interesting in its own right," noting that "the patient reader will be richly rewarded."
Suitable for graduate-level courses, the text begins with three chapters that offer a development of the classical theory along historical lines, examining geometrical and physical considerations, existence theorems for finite Riemann surfaces, and relations between differentials. Subsequent chapters explore bilinear differentials, surfaces imbedded in a given surface, integral operators, and variations of surfaces and of their functionals. The book concludes with a look at applications of the variational method and remarks on generalization to higher dimensional Kahler manifolds.

Menahem Max Schiffer (1911–97) taught at the Hebrew University of Jerusalem, Harvard, and Princeton before joining the faculty at Stanford University, where he was Chairman of the Mathematics Department from 1954 to 1959 and the Robert Grimmett Professor of Mathematics. His previous Dover title is Kernel Functions and Elliptic Differential Equations in Mathematics and Physics.
Donald Clayton Spencer (1921–2001) ranks among the most prominent American mathematicians of his generation. He taught at Princeton and Stanford and collaborated with Kunihiko Kodaira on the modern theory of deformation of complex structures. He is co-author of Dover's Advanced Calculus.