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Menahem Max Schiffer Selected Papers, Volume 2

Peter Duren and Lawrence Zalcman, editors
Publication Date: 
Number of Pages: 
Contemporary Mathematicians
[Reviewed by
Charles Ashbacher
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One does not have to read very many of the papers in this collection to be extremely impressed by the mathematical and writing abilities of Menachem Schiffer. The combined thickness of these two volumes as well as the use of the word “selected” in the title strongly reinforces this impression.

Volume 1 opens with a list of the Schiffer publications, the doctoral students of Schiffer, a chronology of his life and a series of very brief testimonials to Schiffer. Given his impact on mathematics, it is surprising that only 10 pages are devoted to this topic.

The remainder is devoted to reprints of Schiffer’s papers, some of which appear in the original German and French although the majority are in English. Most are followed by a commentary that is in English and approximately one page in length.

Many books about people that had a significant impact on mathematics have a great deal of ink devoted to the person. That is not the case here. Reading these books will expose you to the mathematical output of Menachem Schiffer, but you will learn very little about his life. Given that he left Germany for Palestine in 1933 as a consequence of the rise of the Nazi Party in Germany, there are no doubt some very interesting stories that could be told. 

Charles Ashbacher splits his time between consulting with industry in projects involving math and computers, teaching college classes and co-editing The Journal of Recreational Mathematics. In his spare time, he reads about these things and helps his daughter in her lawn care business.

Part 4: Reprints
The Fredholm eigenvalues of plane domains
Fredholm eigenvalues of multiply-connected domains
Fredholm eigenvalues and conformal mapping
Fredholm eigenvalues and Grunsky matrices
    Commentary by Reiner Kühnau
(with G. Pólya) Sur la représentation conforme de l’extérieur d’une courbe fermée convexe
    Commentary by Peter Duren
Extremum problems and variational methods in conformal mapping
    Commentary by Peter Duren
(with Z. Charzynski) 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

Comments's picture

Readers who share the concerns expressed by the reviewer in his final paragraph will undoubtedly find the final, semi-autobiographical paper published in this volume of particular interest.