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Riemannian geometry / [electronic resource] Robert Greene, S.T. Yau, editors.

Contributor(s): Greene, Robert Everist, 1943- | Yau, Shing-tung, 1949- | Summer Research Institute on Differential Geometry (1990 : University of California, Los Angeles)Material type: Text

TextSeries: Proceedings of symposia in pure mathematics ; v. 54.3Publication details: Providence, R.I. : American Mathematical Society, c1993Description: 1 online resource (xxii, 710 p. : ill.)ISBN: 9780821893548 (online)Subject(s): Geometry, Riemannian -- CongressesAdditional physical formats: Riemannian geometry /DDC classification: 516.3/6 s | 516.3/73 LOC classification: QA641 | .D3833 1993 pt. 3Online resources: Contents | Contents

Partial contents:

Some concepts and methods in Riemannian geometry / Robert E. Greene -- http://www.ams.org/pspum/054.3 http://dx.doi.org/10.1090/pspum/054.3/1216606 Isometric immersions of $H^n$ into $H^{n+1}$ / Kinetsu Abe and Andrew Haas -- http://www.ams.org/pspum/054.3 http://dx.doi.org/10.1090/pspum/054.3/1216607 The distance-geometry of Riemannian manifolds with boundary / Stephanie B. Alexander, I. David Berg and Richard L. Bishop -- http://www.ams.org/pspum/054.3 http://dx.doi.org/10.1090/pspum/054.3/1216608 Hypersurfaces and nonnegative curvature / Stephanie B. Alexander and Robert J. Currier -- http://www.ams.org/pspum/054.3 http://dx.doi.org/10.1090/pspum/054.3/1216609 Shortening space curves / Steven J. Altschuler -- http://www.ams.org/pspum/054.3 http://dx.doi.org/10.1090/pspum/054.3/1216610 Degeneration of metrics with bounded curvature and applications to critical metrics of Riemannian functionals / Michael T. Anderson -- http://www.ams.org/pspum/054.3 http://dx.doi.org/10.1090/pspum/054.3/1216611 The geometry of totally geodesic hypersurfaces in hyperbolic manifolds / Ara Basmajian -- http://www.ams.org/pspum/054.3 http://dx.doi.org/10.1090/pspum/054.3/1216612 Finiteness of diffeomorphism types of isospectral manifolds / Robert Brooks, Peter Perry and Peter Petersen, V -- http://www.ams.org/pspum/054.3 http://dx.doi.org/10.1090/pspum/054.3/1216613 Small eigenvalues of the Laplacian on negatively curved manifolds / P. Buser, B. Colbois and J. Dodziuk -- http://www.ams.org/pspum/054.3 http://dx.doi.org/10.1090/pspum/054.3/1216614 Geometrically tame hyperbolic $3$-manifolds / Richard D. Canary -- http://www.ams.org/pspum/054.3 http://dx.doi.org/10.1090/pspum/054.3/1216615 Isoperimetric constants and large time heat diffusion in Riemannian manifolds / Isaac Chavel and Edgar A. Feldman -- http://www.ams.org/pspum/054.3 http://dx.doi.org/10.1090/pspum/054.3/1216616 Large time behavior of solutions of the heat equation / Isaac Chavel and Leon Karp -- http://www.ams.org/pspum/054.3 http://dx.doi.org/10.1090/pspum/054.3/1216617 Manifolds with 2-nonnegative curvature operator / Haiwen Chen -- http://www.ams.org/pspum/054.3 http://dx.doi.org/10.1090/pspum/054.3/1216618 The geometry of isospectral deformations / Dennis DeTurck, Herman Gluck, Carolyn Gordon and David Webb -- http://www.ams.org/pspum/054.3 http://dx.doi.org/10.1090/pspum/054.3/1216619 Quadric representation of a submanifold and spectral geometry / Ivko Dimitri�c -- http://www.ams.org/pspum/054.3 http://dx.doi.org/10.1090/pspum/054.3/1216620 Embedded eigenvalues for asymptotically flat surfaces / Harold Donnelly -- http://www.ams.org/pspum/054.3 http://dx.doi.org/10.1090/pspum/054.3/1216621 Manifolds of nonpositive curvature / Patrick Eberlein, Ursula Hamenst�adt and Viktor Schroeder -- http://www.ams.org/pspum/054.3 http://dx.doi.org/10.1090/pspum/054.3/1216622 Topological rigidity for compact non-positively curved manifolds / F. T. Farrell and L. E. Jones -- http://www.ams.org/pspum/054.3 http://dx.doi.org/10.1090/pspum/054.3/1216623 Almost non-negatively curved manifolds / Kenji Fukaya and Takao Yamaguchi -- http://www.ams.org/pspum/054.3 http://dx.doi.org/10.1090/pspum/054.3/1216624 Local structure of framed manifolds / Patrick Ghanaat -- http://www.ams.org/pspum/054.3 http://dx.doi.org/10.1090/pspum/054.3/1216625 Constant affine mean curvature hypersurfaces of decomposable type / Salvador Gigena -- http://www.ams.org/pspum/054.3 http://dx.doi.org/10.1090/pspum/054.3/1216626 Heat equation asymptotics / Peter B. Gilkey -- http://www.ams.org/pspum/054.3 http://dx.doi.org/10.1090/pspum/054.3/1216627 Non-negatively curved manifolds which are flat outside a compact set / R. E. Greene and H. Wu -- http://www.ams.org/pspum/054.3 http://dx.doi.org/10.1090/pspum/054.3/1216628 Spaces of nonnegative curvature / Detlef Gromoll -- http://www.ams.org/pspum/054.3 http://dx.doi.org/10.1090/pspum/054.3/1216629 Critical point theory for distance functions / Karsten Grove -- http://www.ams.org/pspum/054.3 http://dx.doi.org/10.1090/pspum/054.3/1216630 Spectral geometry in higher ranks: closed geodesics and flat tori / David Gurarie -- http://www.ams.org/pspum/054.3 http://dx.doi.org/10.1090/pspum/054.3/1216631 Ellipticity of local isometric embeddings / Chong-Kyu Han -- http://www.ams.org/pspum/054.3 http://dx.doi.org/10.1090/pspum/054.3/1216632 Curve flows on surfaces and intersections of curves / Joel Hass and Peter Scott -- http://www.ams.org/pspum/054.3 http://dx.doi.org/10.1090/pspum/054.3/1216633 Curve shortening, equivariant Morse theory, and closed geodesics on the $2$-sphere / Nancy Hingston -- http://www.ams.org/pspum/054.3 http://dx.doi.org/10.1090/pspum/054.3/1216634 Morse theory for geodesics / Diane Kalish -- http://www.ams.org/pspum/054.3 http://dx.doi.org/10.1090/pspum/054.3/1216635 On some metrics on $S^2 \times S^2$ / Masatake Kuranishi -- http://www.ams.org/pspum/054.3 http://dx.doi.org/10.1090/pspum/054.3/1216636 Curve-straightening / Anders Linn�er -- http://www.ams.org/pspum/054.3 http://dx.doi.org/10.1090/pspum/054.3/1216637 Ball covering property and nonnegative Ricci curvature outside a compact set / Zhong-dong Liu -- http://www.ams.org/pspum/054.3 http://dx.doi.org/10.1090/pspum/054.3/1216638 General conjugate loci are not closed / Christophe M. Margerin -- http://www.ams.org/pspum/054.3 http://dx.doi.org/10.1090/pspum/054.3/1216639 Collapsing of Riemannian manifolds and their excesses / Yukio Otsu -- http://www.ams.org/pspum/054.3 http://dx.doi.org/10.1090/pspum/054.3/1216640 Gromov-Hausdorff convergence of metric spaces / Peter Petersen, V -- http://www.ams.org/pspum/054.3 http://dx.doi.org/10.1090/pspum/054.3/1216641 Cartan connections / Ernst A. Ruh -- http://www.ams.org/pspum/054.3 http://dx.doi.org/10.1090/pspum/054.3/1216642 Eigenvalue estimates for the Laplacian with lower order terms on a compact Riemannian manifold / Alberto G. Setti -- http://www.ams.org/pspum/054.3 http://dx.doi.org/10.1090/pspum/054.3/1216643 Positive Ricci curvature on compact simply connected $4$-manifolds / Ji-Ping Sha and DaGang Yang -- http://www.ams.org/pspum/054.3 http://dx.doi.org/10.1090/pspum/054.3/1216644 Volume growth and finite topological type / Zhong Min Shen and Guofang Wei -- http://www.ams.org/pspum/054.3 http://dx.doi.org/10.1090/pspum/054.3/1216645 Recent developments in sphere theorems / Katsuhiro Shiohama -- http://www.ams.org/pspum/054.3 http://dx.doi.org/10.1090/pspum/054.3/1216646 On the excess of open manifolds / Takashi Shioya -- http://www.ams.org/pspum/054.3 http://dx.doi.org/10.1090/pspum/054.3/1216647 Local theory of affine $2$-spheres / U. Simon and C. P. Wang -- http://www.ams.org/pspum/054.3 http://dx.doi.org/10.1090/pspum/054.3/1216648 Riemannian manifolds with completely integrable geodesic flows / R. J. Spatzier -- http://www.ams.org/pspum/054.3 http://dx.doi.org/10.1090/pspum/054.3/1216649 Differentiable structure on spheres and curvature / Yoshihiko Suyama -- http://www.ams.org/pspum/054.3 http://dx.doi.org/10.1090/pspum/054.3/1216650 Spectral theory for operator families on Riemannian manifolds / Z. I.

Szabo -- http://www.ams.org/pspum/054.3 http://dx.doi.org/10.1090/pspum/054.3/1216651 Riemannian foliations and tautness / Philippe Tondeur -- http://www.ams.org/pspum/054.3 http://dx.doi.org/10.1090/pspum/054.3/1216652 Eigenvalue problems for manifolds with singularities / Johan Tysk -- http://www.ams.org/pspum/054.3 http://dx.doi.org/10.1090/pspum/054.3/1216653 Some rigidity aspects of Riemannian fibrations / Gerard Walschap -- http://www.ams.org/pspum/054.3 http://dx.doi.org/10.1090/pspum/054.3/1216654 Hausdorff convergence and sphere theorems / Jyh Yang Wu -- http://www.ams.org/pspum/054.3 http://dx.doi.org/10.1090/pspum/054.3/1216655

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"Proceedings of the Summer Research Institute on Differential Geometry, held at the University of California, Los Angeles, July 8-28, 1990"--T.p. verso.

Includes bibliographical references.

Some concepts and methods in Riemannian geometry / Robert E. Greene -- Isometric immersions of $H^n$ into $H^{n+1}$ / Kinetsu Abe and Andrew Haas -- The distance-geometry of Riemannian manifolds with boundary / Stephanie B. Alexander, I. David Berg and Richard L. Bishop -- Hypersurfaces and nonnegative curvature / Stephanie B. Alexander and Robert J. Currier -- Shortening space curves / Steven J. Altschuler -- Degeneration of metrics with bounded curvature and applications to critical metrics of Riemannian functionals / Michael T. Anderson -- The geometry of totally geodesic hypersurfaces in hyperbolic manifolds / Ara Basmajian -- Finiteness of diffeomorphism types of isospectral manifolds / Robert Brooks, Peter Perry and Peter Petersen, V -- Small eigenvalues of the Laplacian on negatively curved manifolds / P. Buser, B. Colbois and J. Dodziuk -- Geometrically tame hyperbolic $3$-manifolds / Richard D. Canary -- Isoperimetric constants and large time heat diffusion in Riemannian manifolds / Isaac Chavel and Edgar A. Feldman -- Large time behavior of solutions of the heat equation / Isaac Chavel and Leon Karp -- Manifolds with 2-nonnegative curvature operator / Haiwen Chen -- The geometry of isospectral deformations / Dennis DeTurck, Herman Gluck, Carolyn Gordon and David Webb -- Quadric representation of a submanifold and spectral geometry / Ivko Dimitri�c -- Embedded eigenvalues for asymptotically flat surfaces / Harold Donnelly -- Manifolds of nonpositive curvature / Patrick Eberlein, Ursula Hamenst�adt and Viktor Schroeder -- Topological rigidity for compact non-positively curved manifolds / F. T. Farrell and L. E. Jones -- Almost non-negatively curved manifolds / Kenji Fukaya and Takao Yamaguchi -- Local structure of framed manifolds / Patrick Ghanaat -- Constant affine mean curvature hypersurfaces of decomposable type / Salvador Gigena -- Heat equation asymptotics / Peter B. Gilkey -- Non-negatively curved manifolds which are flat outside a compact set / R. E. Greene and H. Wu -- Spaces of nonnegative curvature / Detlef Gromoll -- Critical point theory for distance functions / Karsten Grove -- Spectral geometry in higher ranks: closed geodesics and flat tori / David Gurarie -- Ellipticity of local isometric embeddings / Chong-Kyu Han -- Curve flows on surfaces and intersections of curves / Joel Hass and Peter Scott -- Curve shortening, equivariant Morse theory, and closed geodesics on the $2$-sphere / Nancy Hingston -- Morse theory for geodesics / Diane Kalish -- On some metrics on $S^2 \times S^2$ / Masatake Kuranishi -- Curve-straightening / Anders Linn�er -- Ball covering property and nonnegative Ricci curvature outside a compact set / Zhong-dong Liu -- General conjugate loci are not closed / Christophe M. Margerin -- Collapsing of Riemannian manifolds and their excesses / Yukio Otsu -- Gromov-Hausdorff convergence of metric spaces / Peter Petersen, V -- Cartan connections / Ernst A. Ruh -- Eigenvalue estimates for the Laplacian with lower order terms on a compact Riemannian manifold / Alberto G. Setti -- Positive Ricci curvature on compact simply connected $4$-manifolds / Ji-Ping Sha and DaGang Yang -- Volume growth and finite topological type / Zhong Min Shen and Guofang Wei -- Recent developments in sphere theorems / Katsuhiro Shiohama -- On the excess of open manifolds / Takashi Shioya -- Local theory of affine $2$-spheres / U. Simon and C. P. Wang -- Riemannian manifolds with completely integrable geodesic flows / R. J. Spatzier -- Differentiable structure on spheres and curvature / Yoshihiko Suyama -- Spectral theory for operator families on Riemannian manifolds / Z. I.