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| Hardcover ISBN: | 978-0-8218-1470-3 |
| Product Code: | PSPUM/44 |
| List Price: | $139.00 |
| MAA Member Price: | $125.10 |
| AMS Member Price: | $111.20 |
| eBook ISBN: | 978-0-8218-9336-4 |
| Product Code: | PSPUM/44.E |
| List Price: | $135.00 |
| MAA Member Price: | $121.50 |
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| Hardcover ISBN: | 978-0-8218-1470-3 |
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Book DetailsProceedings of Symposia in Pure MathematicsVolume: 44; 1986; 464 ppMSC: Primary 00; Secondary 28; 49; 53
These twenty-six 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 higher-dimensional 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 measure-theoretic 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 multiple-valued function techniques as a basic new tool in geometric analysis, highlighted by Almgren's fundamental paper Deformations and multiple-valued 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 Navier-Stokes 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
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Articles
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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 ]
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F. Almgren — Deformations and multiple-valued functions [ MR 840268 ]
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Michael T. Anderson — Local estimates for minimal submanifolds in dimensions greater than two [ MR 840269 ]
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John E. Brothers — Second variation estimates for minimal orbits [ MR 840270 ]
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Richard W. Carey and Joel D. Pincus — Index theory for operator ranges and geometric measure theory [ MR 840271 ]
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Paul Concus and Mario Miranda — MACSYMA and minimal surfaces [ MR 840272 ]
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Pierre Dolbeault — Sur les chaînes maximalement complexes de bord donné [ MR 840273 ]
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Robert Gulliver — Index and total curvature of complete minimal surfaces [ MR 840274 ]
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Robert Gulliver and H. Blaine Lawson, Jr. — The structure of stable minimal hypersurfaces near a singularity [ MR 840275 ]
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Robert M. Hardt and David Kinderlehrer — Some regularity results in plasticity [ MR 840276 ]
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Robert M. Hardt and Fang-Hua Lin — Tangential regularity near the $\mathcal {C}^1$-boundary [ MR 840277 ]
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Robert M. Hardt and Jon T. Pitts — Solving Plateau’s problem for hypersurfaces without the compactness theorem for integral currents [ MR 840278 ]
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F. Reese Harvey and H. Blaine Lawson, Jr. — Complex analytic geometry and measure theory [ MR 840279 ]
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Gerhard Huisken — Mean curvature contraction of convex hypersurfaces [ MR 840280 ]
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John E. Hutchinson — $C^{1,\alpha }$ multiple function regularity and tangent cone behaviour for varifolds with second fundamental form in $L^p$ [ MR 840281 ]
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Christophe Margerin — Pointwise pinched manifolds are space forms [ MR 840282 ]
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Dana Nance — The multiplicity of generic projections of $n$-dimensional surfaces in $\mathbf {R}^{n+k}$ $(n+k\leq 4)$ [ MR 840283 ]
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Seiki Nishikawa — Deformation of Riemannian metrics and manifolds with bounded curvature ratios [ MR 840284 ]
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George Paulik — A regularity condition at the boundary for weak solutions of some nonlinear elliptic systems [ MR 840285 ]
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Vladimir Scheffer — Solutions to the Navier-Stokes inequality with singularities on a Cantor set [ MR 840286 ]
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Leon Simon — Asymptotic behaviour of minimal submanifolds and harmonic maps [ MR 840287 ]
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Jean E. Taylor — Complete catalog of minimizing embedded crystalline cones [ MR 840288 ]
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S. Walter Wei — Liouville theorems for stable harmonic maps into either strongly unstable, or $\delta $-pinched, manifolds [ MR 840289 ]
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Brian White — A regularity theorem for minimizing hypersurfaces modulo $p$ [ MR 840290 ]
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William P. Ziemer — Regularity of quasiminima and obstacle problems [ MR 840291 ]
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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 ]
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These twenty-six 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 higher-dimensional 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 measure-theoretic 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 multiple-valued function techniques as a basic new tool in geometric analysis, highlighted by Almgren's fundamental paper Deformations and multiple-valued 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 Navier-Stokes 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 multiple-valued 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 Fang-Hua 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 Navier-Stokes 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 ]
