| Description |
1 online resource (xiii, 497 pages) |
| Contents |
A Summary of the Scientific Activities -- Summary of the Papers in this Volume -- The Cohomology Ring of Certain Kählerian Manifolds -- Isometric immersions with semi-definite second quadratic forms -- Minimal Submanifolds of a Sphere with Second Fundamental Form of Constant Length -- Rigidity and Convexity of Hypersurfaces in Spheres -- Brief Survey Of Minimal Submanifolds II -- Minimal immersions of spheres into spheres -- Spherical Images of Convex Surfaces -- On the Size of a Stable Minimal Surface in R3 -- On Minimal Immersions with Parallel Normal Curvature Tensor -- Minimal Surfaces: Stability and Finiteness -- A Proof of a General Isoperimetric Inequality for Surfaces -- Stable Complete Minimal Surfaces in R3 are Planes -- Stability of Minimal Surfaces and Eigenvalues of the Laplacian -- Stability Of Minimal Submanifolds -- Rotation Hypersurfaces in Spaces of Constant Curvature -- Stability of Hypersurfaces with Constant Mean Curvature -- Compact Conformally Flat Hypersurfaces -- The influence of the boundary behaviour on hypersurfaces with constant mean curvature in Hn+1 -- Conformal Rigidity -- Stability of Hypersurfaces of Constant Mean Curvature in Riemannian Manifolds -- Hypersurfaces of Constant Mean Curvature -- Stable Hypersurfaces with Constant Scalar Curvature -- Hypersurfaces With Constant Mean Curvature in Spheres -- Complete Hypersurfaces with Constant Mean Curvature and Finite Total Curvature -- Research on Differential Geometry in Brazil -- Eigenvalues Estimates on Complete Noncompact Riemannian Manifolds and Applications -- Compact minimal hypersurfaces with index one in the real projective space -- Ricci curvature and the topology of open manifolds -- Stability of hypersurfaces with vanishing r-mean curvature in euclidean space -- A theorem of Hopf and the Cauchy-Riemann inequality -- A Hopf theorem for open surfaces in product spaces -- A Hopf Theorem for Ambient Spaces of Dimensions Higher than Three |
| Summary |
This volume of selected academic papers demonstrates the significance of the contribution to mathematics made by Manfredo P. do Carmo. Twice a Guggenheim Fellow and the winner of many prestigious national and international awards, the professor at the institute of Pure and Applied Mathematics in Rio de Janeiro is well known as the author of influential textbooks such as Differential Geometry of Curves and Surfaces. The area of differential geometry is the main focus of this selection, though it also contains do Carmo's own commentaries on his life as a scientist as well as assessment of the impact of his researches and a complete list of his publications. Aspects covered in the featured papers include relations between curvature and topology, convexity and rigidity, minimal surfaces, and conformal immersions, among others. Offering more than just a retrospective focus, the volume deals with subjects of current interest to researchers, including a paper co-authored with Frank Warner on the convexity of hypersurfaces in space forms. It also presents the basic stability results for minimal surfaces in the Euclidean space obtained by the author and his collaborators. Edited by do Carmo's first student, now a celebrated academic in her own right, this collection pays tribute to one of the most distinguished mathematicians |
| Analysis |
Mathematics |
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Geometry |
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Global differential geometry |
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Differential Geometry |
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History of Mathematical Sciences |
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Manifolds and Cell Complexes (incl. Diff. Topology) |
| Bibliography |
Includes bibliographical references |
| Subject |
Geometry, Differential.
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Mathematics.
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Mathematics
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applied mathematics.
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mathematics.
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MATHEMATICS -- Geometry -- General.
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Geometría diferencial
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Matemáticas
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Mathematics
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Geometry, Differential
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| Form |
Electronic book
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| Author |
Tenenblat, Keti.
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| ISBN |
9783642255885 |
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3642255884 |
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