# Selected Works of Frederick J. Almgren, Jr (Collected Works)

By: Frederick J. Almgren (author), Jean E. Taylor (volume_editor)Hardback

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### Description

This volume offers a unique collection of some of the work of Frederick J. Almgren, Jr., the man most noted for defining the shape of geometric variational problems and for his role in founding The Geometry Center. Included in the volume are the following: a summary by Sheldon Chang of the famous 1700 page paper on singular sets of area-minimizing $m$-dimensional surfaces in $R^n$, a detailed summary by Brian White of Almgren's contributions to mathematics, his own announcements of several longer papers, important shorter papers, and memorable expository papers.Almgren's enthusiasm for the subject and his ability to locate mathematically beautiful problems that were 'ready to be solved' attracted many students who further expanded the subject into new areas. Many of these former students are now known for the clarity of their expositions and for the beauty of the problems that they work on. As Almgren's former graduate student, wife, and colleague, Professor Taylor has compiled an important volume on an extraordinary mathematician. This collection presents a fine comprehensive view of the man's mathematical legacy.

### Contents

The mathematics of F. J. Almgren, Jr. by B. White On Almgren's regularity result by S. X. Chang The homotopy groups of the integral cycle groups by F. J. Almgren, Jr. An isoperimetric inequality by F. J. Almgren, Jr. Three theorems on manifolds with bounded mean curvature by F. J. Almgren, Jr. Existence and regularity almost everywhere of solutions to elliptic variational problems among surfaces of varying topological type and singularity structure by F. J. Almgren, Jr. Measure theoretic geometry and elliptic variational problems by F. J. Almgren, Jr. The structure of limit varifolds associated with minimizing sequences of mappings by F. J. Almgren, Jr. Existence and regularity almost everywhere of solutions to elliptic variational problems with constraints by F. J. Almgren, Jr. The structure of stationary one dimensional varifolds with positive density by W. K. Allard and F. J. Almgren, Jr. The geometry of soap films and soap bubbles by F. J. Almgren, Jr. and J. E. Taylor Examples of unknotted curves which bound only surfaces of high genus within their convex hulls by F. J. Almgren, Jr. and W. P. Thurston Regularity and singularity estimates on hypersurfaces minimizing parametric elliptic variational integrals by R. Schoen, L. Simon, and F. J. Almgren, Jr. Dirichlet's problem for multiple valued functions and the regularity of mass minimizing integral currents by F. J. Almgren, Jr. Liquid crystals and geodesics by R. N. Thurston and F. J. Almgren $\mathbf{Q}$ valued functions minimizing Dirichlet's integral and the regularity of area minimizing rectifiable currents up to codimension two by F. J. Almgren, Jr. Optimal isoperimetric inequalities by F. Almgren Co-area, liquid crystals, and minimal surfaces by F. Almgren, W. Browder, and E. Lieb Singularities of energy minimizing maps from the ball to the sphere: Examples, counterexamples, and bounds by F. J. Almgren, Jr. and E. H. Lieb Symmetric decreasing rearrangement is sometimes continuous by F. J. Almgren, Jr. and E. H. Lieb Questions and answers about area-minimizing surfaces and geometric measure theory by F. Almgren Curvature-driven flows: A variational approach by F. Almgren, J. E. Taylor, and L. Wang Questions and answers about geometric evolution processes and crystal growth by F. Almgren.

### Product Details

• ISBN13: 9780821810675
• Format: Hardback
• Number Of Pages: 586
• ID: 9780821810675
• ISBN10: 0821810677

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