Menahem Max Schiffer: Selected Papers Volume 2

Menahem Max Schiffer, a mathematician of many interests, produced a body of work including topics on geometric function theory, Riemann surfaces, and partial differential equations, with a focus on applications and mathematical physics. Perhaps his best known work is that in the calculus of variations, especially extremal problems, which find application in many scientific areas.

This two volume set presents over 50 of the most groundbreaking contributions of this beloved mathematician. All of the reprints of Schiffer’s works herein have extensive annotation and invited commentaries, giving new clarity and insight into the impact and legacy of Schiffer's works. A complete bibliography and brief biography make this a rounded and invaluable reference.

M. M. Schiffer, the dominant figure in geometric function theory in the second half of the twentieth century, was a mathematician of exceptional breadth, whose work ranged over such areas as univalent functions, conformal mapping, Riemann surfaces, partial differential equations, potential theory, fluid dynamics, and the theory of relativity. He is best remembered for the powerful variational methods he developed and applied to extremal problems in a wide variety of scientific fields.

Spanning seven decades, the papers collected in these two volumes represent some of Schiffer's most enduring innovations. Expert commentaries provide valuable background and survey subsequent developments. Also included are a complete bibliography and several appreciations of Schiffer's influence by collaborators and other admirers.

Part 4: Reprints.- The Fredholm eigen values of plane domains.- Fredholm eigen values of multiply-connected domains.- Fredholm eigenvalues and conformal mapping.- Fredholm eigenvalues and Grunsky matrices.- Commentary by Reiner K¨uhnau.- (with G. P´olya) Sur la repr´esentation conforme de l’ext´erieur d’une courbe ferm´ee convexe.- Commentary by Peter Duren.- Extremum problems and variational methods in conformal mapping.- Commentary by Peter Duren.- (with Z. Charzy´nski) A new proof of the Bieberbach conjecture for the fourth Coefficient.- Commentary by Peter Duren.- (with P. L. Duren) A variational method for functions schlicht in an annulus.- Commentary by Peter Duren.- (with B. Epstein) On the mean-value property of harmonic functions.- Commentary by Lawrence Zalcman.- (with N. S. Hawley) Half-order differentials on Riemann surfaces.- Commentary by John Fay.- (with P. R. Garabedian) The local maximum theorem for the coefficients of univalent functions.- Commentary by Peter Duren.- Some distortion theorems in the theory of conformal mapping.- Commentary by Peter Duren.- (with G. Schober) An extremal problem for the Fredholm eigenvalues.- (with G. Schober) A remark on the paper “An extremal problem for the Fredholm eigenvalues”.- (with G. Schober) A variational method for general families of quasiconformal mappings.- Commentary by Reiner Kühnau.- (with J. Hersch and L. E. Payne) Some inequalities for Stekloff eigenvalues.- Commentary by Bodo Dittmar.- (with J. A. Hummel) Variational methods for Bieberbach-Eilenberg functions and for pairs.- Commentary by Dov Aharonov.- (with J. A. Hummel and B. Pinchuk) Bounded univalent functions which cover a fixed disc.- Commentary by Bernard Pinchuk.- (with G. Schober) The dielectric Green’s function and quasiconformal mapping.- Commentary by Brad Osgood.- (with A. Chang and G. Schober) On the second variation for univalent functions.- Commentary by Peter Duren.- (with D. Aharonov and L. Zalcman)Potato kugel.- Commentary by Lawrence Zalcman.- (with P. L. Duren and Y. J. Leung) Support points with maximum radial angle.- Commentary by Peter Duren.- (with P. L. Duren) Univalent functions which map onto regions of given transfinite diameter.- Commentary by Peter Duren.- (with P. L. Duren) Robin functions and distortion of capacity under conformal mapping.- Commentary by Peter Duren.- Issai Schur: Some personal reminiscences.- Commentary by Lawrence Zalcman.