Hardcover ISBN:  9780821814703 
Product Code:  PSPUM/44 
List Price:  $102.00 
MAA Member Price:  $91.80 
AMS Member Price:  $81.60 
Electronic ISBN:  9780821893364 
Product Code:  PSPUM/44.E 
List Price:  $96.00 
MAA Member Price:  $86.40 
AMS Member Price:  $76.80 

Book DetailsProceedings of Symposia in Pure MathematicsVolume: 44; 1986; 464 ppMSC: Primary 00; Secondary 28; 49; 53;
These twentysix papers survey a cross section of current work in modern geometric measure theory and its applications in the calculus of variations. Presently the field consists of a jumble of new ideas, techniques and intuitive hunches; an exchange of information has been hindered, however, by the characteristic length and complexity of formal research papers in higherdimensional geometric analysis. This volume provides an easier access to the material, including introductions and summaries of many of the authors' much longer works and a section containing 80 open problems in the field. The papers are aimed at analysts and geometers who may use geometric measuretheoretic techniques, and they require a mathematical sophistication at the level of a second year graduate student.
The papers included were presented at the 1984 AMS Summer Research Institute held at Humboldt State University. A major theme of this institute was the introduction and application of multiplevalued function techniques as a basic new tool in geometric analysis, highlighted by Almgren's fundamental paper Deformations and multiplevalued functions. Major new results discussed at the conference included the following: Allard's integrality and regularity theorems for surfaces stationary with respect to general elliptic integrands; Scheffer's first example of a singular solution to the NavierStokes equations for a fluid flow with opposing force; and Hutchinson's new definition of the second fundamental form of a general varifold.Readership 
Table of Contents

Articles

William K. Allard  An integrality theorem and a regularity theorem for surfaces whose first variation with respect to a parametric elliptic integrand is controlled [ MR 840267 ]

F. Almgren  Deformations and multiplevalued functions [ MR 840268 ]

Michael T. Anderson  Local estimates for minimal submanifolds in dimensions greater than two [ MR 840269 ]

John E. Brothers  Second variation estimates for minimal orbits [ MR 840270 ]

Richard W. Carey and Joel D. Pincus  Index theory for operator ranges and geometric measure theory [ MR 840271 ]

Paul Concus and Mario Miranda  MACSYMA and minimal surfaces [ MR 840272 ]

Pierre Dolbeault  Sur les chaînes maximalement complexes de bord donné [ MR 840273 ]

Robert Gulliver  Index and total curvature of complete minimal surfaces [ MR 840274 ]

Robert Gulliver and H. Blaine Lawson, Jr.  The structure of stable minimal hypersurfaces near a singularity [ MR 840275 ]

Robert M. Hardt and David Kinderlehrer  Some regularity results in plasticity [ MR 840276 ]

Robert M. Hardt and FangHua Lin  Tangential regularity near the $\mathcal {C}^1$boundary [ MR 840277 ]

Robert M. Hardt and Jon T. Pitts  Solving Plateau’s problem for hypersurfaces without the compactness theorem for integral currents [ MR 840278 ]

F. Reese Harvey and H. Blaine Lawson, Jr.  Complex analytic geometry and measure theory [ MR 840279 ]

Gerhard Huisken  Mean curvature contraction of convex hypersurfaces [ MR 840280 ]

John E. Hutchinson  $C^{1,\alpha }$ multiple function regularity and tangent cone behaviour for varifolds with second fundamental form in $L^p$ [ MR 840281 ]

Christophe Margerin  Pointwise pinched manifolds are space forms [ MR 840282 ]

Dana Nance  The multiplicity of generic projections of $n$dimensional surfaces in $\mathbf {R}^{n+k}$ $(n+k\leq 4)$ [ MR 840283 ]

Seiki Nishikawa  Deformation of Riemannian metrics and manifolds with bounded curvature ratios [ MR 840284 ]

George Paulik  A regularity condition at the boundary for weak solutions of some nonlinear elliptic systems [ MR 840285 ]

Vladimir Scheffer  Solutions to the NavierStokes inequality with singularities on a Cantor set [ MR 840286 ]

Leon Simon  Asymptotic behaviour of minimal submanifolds and harmonic maps [ MR 840287 ]

Jean E. Taylor  Complete catalog of minimizing embedded crystalline cones [ MR 840288 ]

S. Walter Wei  Liouville theorems for stable harmonic maps into either strongly unstable, or $\delta $pinched, manifolds [ MR 840289 ]

Brian White  A regularity theorem for minimizing hypersurfaces modulo $p$ [ MR 840290 ]

William P. Ziemer  Regularity of quasiminima and obstacle problems [ MR 840291 ]

Edited by John E. Brothers  Some open problems in geometric measure theory and its applications suggested by participants of the 1984 AMS summer institute [ MR 840292 ]


Request Review Copy

Get Permissions
 Book Details
 Table of Contents

 Request Review Copy
 Get Permissions
These twentysix papers survey a cross section of current work in modern geometric measure theory and its applications in the calculus of variations. Presently the field consists of a jumble of new ideas, techniques and intuitive hunches; an exchange of information has been hindered, however, by the characteristic length and complexity of formal research papers in higherdimensional geometric analysis. This volume provides an easier access to the material, including introductions and summaries of many of the authors' much longer works and a section containing 80 open problems in the field. The papers are aimed at analysts and geometers who may use geometric measuretheoretic techniques, and they require a mathematical sophistication at the level of a second year graduate student.
The papers included were presented at the 1984 AMS Summer Research Institute held at Humboldt State University. A major theme of this institute was the introduction and application of multiplevalued function techniques as a basic new tool in geometric analysis, highlighted by Almgren's fundamental paper Deformations and multiplevalued functions. Major new results discussed at the conference included the following: Allard's integrality and regularity theorems for surfaces stationary with respect to general elliptic integrands; Scheffer's first example of a singular solution to the NavierStokes equations for a fluid flow with opposing force; and Hutchinson's new definition of the second fundamental form of a general varifold.

Articles

William K. Allard  An integrality theorem and a regularity theorem for surfaces whose first variation with respect to a parametric elliptic integrand is controlled [ MR 840267 ]

F. Almgren  Deformations and multiplevalued functions [ MR 840268 ]

Michael T. Anderson  Local estimates for minimal submanifolds in dimensions greater than two [ MR 840269 ]

John E. Brothers  Second variation estimates for minimal orbits [ MR 840270 ]

Richard W. Carey and Joel D. Pincus  Index theory for operator ranges and geometric measure theory [ MR 840271 ]

Paul Concus and Mario Miranda  MACSYMA and minimal surfaces [ MR 840272 ]

Pierre Dolbeault  Sur les chaînes maximalement complexes de bord donné [ MR 840273 ]

Robert Gulliver  Index and total curvature of complete minimal surfaces [ MR 840274 ]

Robert Gulliver and H. Blaine Lawson, Jr.  The structure of stable minimal hypersurfaces near a singularity [ MR 840275 ]

Robert M. Hardt and David Kinderlehrer  Some regularity results in plasticity [ MR 840276 ]

Robert M. Hardt and FangHua Lin  Tangential regularity near the $\mathcal {C}^1$boundary [ MR 840277 ]

Robert M. Hardt and Jon T. Pitts  Solving Plateau’s problem for hypersurfaces without the compactness theorem for integral currents [ MR 840278 ]

F. Reese Harvey and H. Blaine Lawson, Jr.  Complex analytic geometry and measure theory [ MR 840279 ]

Gerhard Huisken  Mean curvature contraction of convex hypersurfaces [ MR 840280 ]

John E. Hutchinson  $C^{1,\alpha }$ multiple function regularity and tangent cone behaviour for varifolds with second fundamental form in $L^p$ [ MR 840281 ]

Christophe Margerin  Pointwise pinched manifolds are space forms [ MR 840282 ]

Dana Nance  The multiplicity of generic projections of $n$dimensional surfaces in $\mathbf {R}^{n+k}$ $(n+k\leq 4)$ [ MR 840283 ]

Seiki Nishikawa  Deformation of Riemannian metrics and manifolds with bounded curvature ratios [ MR 840284 ]

George Paulik  A regularity condition at the boundary for weak solutions of some nonlinear elliptic systems [ MR 840285 ]

Vladimir Scheffer  Solutions to the NavierStokes inequality with singularities on a Cantor set [ MR 840286 ]

Leon Simon  Asymptotic behaviour of minimal submanifolds and harmonic maps [ MR 840287 ]

Jean E. Taylor  Complete catalog of minimizing embedded crystalline cones [ MR 840288 ]

S. Walter Wei  Liouville theorems for stable harmonic maps into either strongly unstable, or $\delta $pinched, manifolds [ MR 840289 ]

Brian White  A regularity theorem for minimizing hypersurfaces modulo $p$ [ MR 840290 ]

William P. Ziemer  Regularity of quasiminima and obstacle problems [ MR 840291 ]

Edited by John E. Brothers  Some open problems in geometric measure theory and its applications suggested by participants of the 1984 AMS summer institute [ MR 840292 ]