Differential Geometry Parts 1-3 (Proceedings of Symposia in Pure Mathematics)

Differential Geometry Parts 1-3 (Proceedings of Symposia in Pure Mathematics)


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These three parts contain the proceedings of the AMS Summer Institute on Differential Geometry, held at the University California, Los Angeles in July 1990. This was the largest AMS Summer Institute ever, reflecting the wide-ranging and intense research activity in the subject. The parts contain many extensive survey articles presenting perspectives on relatively broad topics; these articles would be accessible to advanced graduate students. In addition, the authors of the research articles were encouraged to survey the relevant literature. The three parts together offer the deepest and most comprehensive survey of recent research in differential geometry available today.


Part 1. Partial Differential Equations on Manifolds: Open problems in geometry by S. T. Yau Questions and answers about area-minimizing surfaces and geometric measure theory by F. Almgren On the geometrical origin and the solutions of a degenerate Monge-Ampere equation by D. Bao and T. Ratiu Differential geometry and the design of gradient algorithms by R. W. Brockett Spectral geometry of $V$-manifolds and its application to harmonic maps by Y.-J. Chiang Constructing harmonic maps into the hyperbolic space by H. I. Choi and A. Treibergs Spherical minimal immersions of spherical space forms by D. DeTurck and W. Ziller Banach manifolds of solutions to nonlinear partial differential equations, and relations with finite-dimensional manifolds by J. Dorfmeister Some new harmonic maps by R. Hardt Existence of unstable minimal surfaces in manifolds with homology and applications to triply periodic minimal surfaces by J. Hass, J. T. Pitts, and J. H. Rubinstein Closed minimal submanifolds in the spheres by W.-Y. Hsiang Local and global behaviour of hypersurfaces moving by mean curvature by G. Huisken The level-set flow on a manifold by T. Ilmanen Unstable solutions of two-dimensional geometric variational problems by J. Jost Harmonic maps and superrigidity by J. Jost and S. T. Yau Harmonic functions of polynomial growth on complete manifolds by A. Kasue The structure of constant mean curvature embeddings in Euclidean three space by N. Korevaar and R. Kusner Uniformization of spherical CR manifolds and the CR Yamabe problem by Z. Li The theory of harmonic functions and its relation to geometry by P. Li Harmonic maps with prescribed singularities by Y. Y. Li and G. Tian Some recent results on harmonic maps to spheres by F. H. Lin The geometry, topology, and existence of periodic minimal surfaces by W. H. Meeks III Soap films and mathematics by F. Morgan Uniform boundary regularity estimates for minima of certain quadratic functionals by L. H. Mou Self-similar solutions and asymptotic behavior of flows of nonparametric surfaces driven by Gauss or mean curvature by V. Oliker A report on geometric quantization by P. L. Robinson Motion of curves by crystalline curvature, including triple junctions and boundary points by J. E. Taylor Recent progress in submanifold geometry by C.-L. Terng Constant mean curvature surfaces in the Heisenberg group by P. Tomter Complete immersions of constant mean curvature by H. C. Wente Banach manifolds of minimal surfaces in the 4-sphere by H. Wu On the isolatedness for the solutions of Plateau's problem by S. Zheng Part 2. Geometry in Mathematical Physics and Related Topics: Invariants of Gauss maps of theta divisors by M. Adams, C. McCrory, T. Shifrin, and R. Varley On characteristics of hypersurfaces in symplectic manifolds by A. Banyaga Disprisoning and pseudoconvex manifolds by J. K. Beem On the holonomy of Lorentzian manifolds by L. B. Bergery and A. Ikemakhen Spinors, Dirac operators, and changes of metrics by J.-P. Bourguignon The Hyperkahler geometry of the ADHM construction and quaternionic geometric invariant theory by C. P. Boyer and B. M. Mann Non-abelian vortices and a new Yang-Mills-Higgs energy by S. B. Bradlow What are the best almost-complex structures on the 6-sphere? by E. Calabi and H. Gluck The failure of complex and symplectic manifolds to be Kahlerian by L. A. Cordero, M. Fernandez, and A. Gray Nonabelian Hodge theory by K. Corlette Geometric invariants and their adiabatic limits by X. Dai Geometry of elementary particles by A. Derdzinski Existence of connections with prescribed Yang-Mills currents by D. DeTurck, H. Goldschmidt, and J. Talvacchia Vector bundles over homogeneous spaces and complete, locally symmetric spaces by L. D. Drager and R. L. Foote Margulis space-times by T. A. Drumm Incomplete flat homogeneous geometries by D. Duncan and E. Ihrig Geodesic and causal behavior of gravitational plane waves: astigmatic conjugacy by P. E. Ehrlich and G. G. Emch Curvature of singular spaces via the normal cycle by J. H. G. Fu The nonintegrable phase factor and gauge theory by R. O. Fulp The Lorentzian version of the Cheeger-Gromoll splitting theorem and its application to general relativity by G. J. Galloway Weyl structures on self-dual conformal manifolds by P. Gauduchon Chiral anomalies and Dirac families in Riemannian foliations by J. F. Glazebrook and F. W. Kamber What is the shape of space in a spacetime? by S. G. Harris The kinematics of the gravitational field by A. D. Helfer Support theorems in integral geometry and their applications by S. Helgason Killing spinors and eigenvalues of the; Dirac operator by O. Hijazi Einstein metrics on circle bundles by G. R. Jensen and M. Rigoli Topological and differentiable structures of the complement of an arrangement of hyperplanes by T. Jiang and S. S.-T. Yau The relationship between the moduli spaces of vector bundles on $K3$ surfaces and Enriques surfaces by H. Kim Self-dual manifolds with symmetry by C. LeBrun and Y. S. Poon Remarks on the Skyrme model by E. H. Lieb Geometric settings for quantum systems with isospin by E. B. Lin Heat kernels on covering spaces and topological invariants by J. Lott The heat kernels of symmetric spaces by Q.-K. Lu CR-geometry and deformations of isolated singularities by J. J. Millson Generalized symplectic geometry on the frame bundle of a manifold by L. K. Norris Complex geometry and string theory by D. H. Phong Constructing non-self-dual Yang-Mills connections on $S^4$ with arbitrary Chern number by L. Sadun and J. Segert The Yang-Mills measure for the two-sphere by A. Sengupta Examples of nonminimal critical points in gauge theory by L. M. Sibner Spectral invariants of pseudoconformal manifolds by N. K. Stanton $L 2$-cohomology and index theory of noncompact manifolds by M. Stern On Calabi-Yau three-folds fibered over smooth complex surfaces by W.-W. Sung Degeneration of Kahler-Einstein manifolds. I by G. Tian Flat connections on products of determinant bundles by Y. L. L. Tong Surfaces Riemanniennes a singularites simples by M. Troyanov Remarks on certain higher-dimensional quasi-Fuchsian domains by S. T. Yau and F. Zheng $L^p$-cohomology: Banach spaces and homological methods on Riemannian manifolds by S. Zucker Part 3. Riemannian Geometry: Some concepts and methods in Riemannian geometry by R. E. Greene Isometric immersions of $H^n$ into $H^n+1$ by K. Abe and A. Haas The distance-geometry of Riemannian manifolds with boundary by S. B. Alexander, I. D. Berg, and R. L. Bishop Hypersurfaces and nonnegative curvature by S. B. Alexander and R. J. Currier Shortening space curves by S. J. Altschuler Degeneration of metrics with bounded curvature and applications to critical metrics of Riemannian functionals by M. T. Anderson The geometry of totally geodesic hypersurfaces in hyperbolic manifolds by A. Basmajian Finiteness of diffeomorphism types of isospectral manifolds by R. Brooks, P. Perry, and P. P. V Small eigenvalues of the Laplacian on negatively curved manifolds by P. Buser, B. Colbois, and J. Dodziuk Geometrically tame hyperbolic $3$-manifolds by R. D. Canary Isoperimetric constants and large time heat diffusion in Riemannian manifolds by I. Chavel and E. A. Feldman Large time behavior of solutions of the heat equation by I. Chavel and L. Karp Manifolds with $2$-nonnegative curvature operator by H. Chen The geometry of isospectral deformations by D. DeTurck, H. Gluck, C. Gordon, and D. Webb Quadric representation of a submanifold and spectral geometry by I. Dimitric Embedded eigenvalues for asymptotically flat surfaces by H. Donnelly Manifolds of nonpositive curvature by P. Eberlein, U. Hamenstadt, and V. Schroeder Topological rigidity for compact nonpositively curved manifolds by F. T. Farrell and L. E. Jones Almost nonnegatively curved manifolds by K. Fukaya and T. Yamaguchi Local structure of framed manifolds by P. Ghanaat Constant affine mean curvature hypersurfaces of decomposable type by S. Gigena Heat equation asymptotics by P. B. Gilkey Nonnegatively curved manifolds which are flat outside a compact set by R. E. Greene and H. Wu Spaces of nonnegative curvature by D. Gromoll Critical point theory for distance functions by K. Grove Spectral geometry in higher ranks: Closed geodesics and flat tori by D. Gurarie Ellipticity of local isometric embeddings by C.-K. Han Curve flows on surfaces and intersections of curves by J. Hass and P. Scott Curve shortening, equivariant Morse theory, and closed geodesics on the $2$-sphere by N. Hingston Morse theory for geodesics by D. Kalish On some metrics on $S^2\times S^2$ by M. Kuranishi Curve-straightening by A. Linner Ball covering property and nonnegative Ricci curvature outside a compact set by Z.-D. Liu General conjugate Loci are not closed by C. M. Margerin Collapsing of Riemannian manifolds and their excesses by Y. Otsu Gromov-Hausdorff convergence of metric spaces by P. P. V Cartan connections by E. A. Ruh Eigenvalue estimates for the Laplacian with lower order terms on a compact Riemannian manifold by A. G. Setti Positive Ricci curvature on compact simply connected $4$-manifolds by J.-P. Sha and D. Yang Volume growth and finite topological type by Z. Shen and G. Wei Recent developments in sphere; theorems by K. Shiohama On the excess of open manifolds by T. Shioya Local theory of affine $2$-spheres by U. Simon and C. P. Wang Riemannian manifolds with completely integrable geodesic flows by R. J. Spatzier Differentiable structure on spheres and curvature by Y. Suyama Spectral theory for operator families on Riemannian manifolds by Z. I. Szabo Riemannian foliations and tautness by P. Tondeur Eigenvalue problems for manifolds with singularities by J. Tysk Some rigidity aspects of Riemannian fibrations by G. Walschap Hausdorff convergence and sphere theorems by J.-Y. Wu Automorphism groups and fundamental groups of geometric manifolds by R. J. Zimmer.

Product Details

  • ISBN13: 9780821814932
  • Format: Hardback
  • Number Of Pages: 3
  • ID: 9780821814932
  • ISBN10: 0821814931

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