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Selected Works of Frederick J. Almgren, Jr.
Edited by: Jean E. Taylor, Rutgers University, New Brunswick, NJ
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Collected Works
1999; 586 pp; hardcover
Volume: 13
ISBN-10: 0-8218-1067-7
ISBN-13: 978-0-8218-1067-5
List Price: US$122
Member Price: US$97.60
Order Code: CWORKS/13
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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.

Readership

Graduate students and research mathematicians interested in geometry, calculus of variations and optimal control and optimization.

Reviews

"The reader is invited to recover throughout this book the beauty of the geometric variational problems treated by this great mathematician during his life, the deep ideas involved in the proofs, the great appeal and clarity of his expository papers ... this book should not be absent from the library of those who are really impassioned by geometric measure theory and the calculus of variations."

-- Mathematical Reviews

Table of Contents

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