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Selected works of Frederick J. Almgren, Jr. Edited by Jean E. Taylor. (English) Zbl 0966.01031
Providence, RI: American Mathematical Society (AMS). xlvi, 586 p. $ 105.00 (1999).

It is well known that mathematicians publish their research works in different journals. On many occasions it becomes impossible to go through the research papers because of non-availability of those aforesaid journals. Hence with the objective to remove this difficulty the publication of the collected or selected works of different mathematicians is imperative, since this will be helpful to present as well as future generations. Thanks to the authorities of the American Mathematical Society for their publication of the selected works of Frederick J. Almgren, Jr who died on February 5, 1997 at the age of 63 due to a sudden devasting illness called myelodysplastic syndrome.

In this selected works there are 21 papers of Almgren. Their titles are as follows: (i) The homotopy groups of the integral cyclic groups, (ii) An isoperimetric inequality, (iii) Three theorems on manifolds with bounded mean curvature, (iv) Existence and regularity almost everywhere of solutions to elliptic variational problems among surfaces of varying topological type and singularity structure, (v) Measure theoretic geometry and elliptic variational problems, (vi) The structure of limit varifolds associated with minimizing sequences of mappings, (vii) Existence and regularity almost everywhere of solutions to elliptic variational problems with constraints, (viii) The structure of stationary one dimensional varifolds with positive density (with William K. Allard), (ix) The geometry of soap films and soap bubbles (with Jean E. Taylor), (x) Examples of unknotted curves which bound only surfaces of high genus with their convex hull (with William P. Thurston),

(xi) Regularity and singularity estimates on hypersurfaces minimizing parametric elliptic variational integrals, (with Richard Schoen and Leon Simon), (xii) Dirichlet’s problem for multiple valued functions and the regularity of mass minimizing integral currents, minimal submanifolds and geodesics, (xiii) Liquid crystals and geodesics (with Robert N. Thurston), (xiv) Q-valued functions minimizing Dirichlet’s integral and regularity of area minimizing rectifiable currents up to codimension two, (xv) Optional isoperimetric inequalities, (xvi) Co-area, liquid crystals and minimal surfaces, partial differential equations (with William Browder and Elliott H. Lieb), (xvii) Singularities of energy minimizing maps from the ball of the sphere (with Elliott H. Lieb), (xviii) Symmetric rearrangement is sometimes continuous (with Elliott H. Lieb), (xix) Questions and answers about area minimizing surfaces and geometric measure theory, Differential Geometry, (xx) Curvature driven flows: A variational approach (with Jean E. Taylor and Lihe Wang), (xxi) Questions and answers about geometric evolution processes and crystal growth.

Besides there are two articles, viz, (i) The Mathematics of Frederick J. Almgren jun. written by Brian White, (ii) On Almgren’s regularity results written by Sheldon X. Chang.

This selected work provides a very useful collection for future generations.

01A75Collected or selected works
01-02Research monographs (history)