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2 edition of Two-dimensional manifolds of bounded curvature found in the catalog.

Two-dimensional manifolds of bounded curvature

A. D. Aleksandrov

Two-dimensional manifolds of bounded curvature

by A. D. Aleksandrov

  • 272 Want to read
  • 16 Currently reading

Published by American Mathematical Society in Providence, R.I .
Written in English

    Subjects:
  • Geometry, Differential.

  • Edition Notes

    Statementedited by A.D. Aleksandrov and V.A. Zalgaller. [Translated from the Russian by J.M. Danskin]
    SeriesProceedings of the Steklov Institute of Mathematics,, no. 76
    ContributionsZalgaller, V. A.
    Classifications
    LC ClassificationsQA1 .A413 no. 76
    The Physical Object
    Paginationiv, 183 p.
    Number of Pages183
    ID Numbers
    Open LibraryOL5532928M
    LC Control Number67009008
    OCLC/WorldCa813229

    The Mathematics of Three-dimensional Manifolds Topological study of these higher-dimensional analogues of a surface suggests the universe may be as convoluted as a tangled loop of string. It now appears most of the manifolds can be analyzed geometrically by William P. Thurston and Jeffrey R. Weeks Thousands of years ago many peo­File Size: KB. The completion of hyperbolic three-manifolds obtained from ideal polyhedra. 54 The generalized Dehn surgery invariant. 56 Dehn surgery on the figure-eight knot. 58 Degeneration of hyperbolic structures. 61 Incompressible surfaces in the figure-eight knot complement. 71 Thurston — The Geometry and Topology of 3 File Size: 4MB.

    In section of his big book on Riemannian geometry, Berger has a discussion on the question of to what degree (and in what sense) the curvature determines the metric. He quotes the following theorem by Cartan on the two-dimensional case. In this paper, we study submanifolds in a Euclidean space with a generalized 1-type Gauss map. The Gauss map, G, of a submanifold in the n-dimensional Euclidean space, E n, is said to be of generalized 1-type if, for the Laplace operator, Δ, on the submanifold, it satisfies Δ G = f G + g C, where C is a constant vector and f and g are some functions. The notion of a generalized 1-type Gauss.

    () The role of the scalar curvature in a nonlinear elliptic problem on Riemannian manifolds. Calculus of Variations and Partial Differential Equations , () Multipeak solutions for some singularly perturbed nonlinear elliptic problems on Riemannian by: "Minimal two-spheres and the topology of manifolds with positive curvature on totally isotropic two-planes" (with Mario Micallef), Annals of Math. v. , pp. "On the number of minimal two-spheres of small area in manifolds with curvature bounded above", Math. Ann. v. , pp.


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Two-dimensional manifolds of bounded curvature by A. D. Aleksandrov Download PDF EPUB FB2

Abstract. The theory of two-dimensional manifolds of bounded curvature is a generalization of two-dimensional Riemannian geometry. Formally a two-dimensional manifold of bounded curvature is a two-dimensional manifold in which there are defined the concepts of the length of a curve, the angle between curves starting from one point, the area of a set, and also the integral curvature of a curve Cited by: Get this from a library.

Two-dimensional manifolds of bounded curvature. [A D Aleksandrov; V A Zalgaller]. Both parts cover topics, which have not yet been treated in monograph form. Hence the book will be immensely useful to graduate students and researchers in geometry, in particular Riemannian geometry.\/span>\"@ en\/a> ; \u00A0\u00A0\u00A0\n schema:description\/a> \" I.

Two-Dimensional Manifolds of Bounded Curvature -- II. The limit spaces of two-dimensional manifolds with uniformly bounded integral curvature, Trans. Amer. Math. Soc. (5) (), – Troyanov, M., Les surfaces à courbure intégrale bornée au sens d’Alexandrov, Journées annuelles de la SMF (), 1 – Cited by: 1.

Formally a two-dimensional manifold of bounded curvature is a two-dimensional manifold in which there are defined the concepts of the length of a curve, the angle between curves starting from one. Even much earlier, Alexan- drov [1] defined the Gauss curvature measure for s.c.

two-dimensional manifolds of bounded integral curvature and this approach has further been developed by Fu in [ We show how Lasry–Lions's result on regularization of functions defined on R n or on Hilbert spaces by sup–inf convolutions with squares of distances can be extended to (finite or infinite dimensional) Riemannian manifolds M of bounded sectional curvature.

More specifically, among other things we show that if the sectional curvature K of M Two-dimensional manifolds of bounded curvature book − K 0 ≤ K ≤ K 0 on M for some K 0 Cited by: 9. Download Book Two Dimensional Man in PDF format.

You can Read Online Two Dimensional Man here in PDF, EPUB, Mobi or Docx formats. Two-dimensional Manifolds of Bounded Curvature. Author: Aleksandr Danilovich Aleksandrov,Viktor A.

Zalgaller. Publisher: American Mathematical Soc. Definition. Suppose that (M, g) is an n-dimensional Riemannian manifold, equipped with its Levi-Civita connection ∇.The Riemannian curvature tensor of M is the (1, 3)-tensor defined by (,) = ∇ ∇ − ∇ ∇ − ∇ [,]on vector fields X, Y, T p M denote the tangent space of M at a point any pair of tangent vectors ξ and η in T p M, the Ricci tensor Ric evaluated at (ξ, η.

The first article written by Reshetnyak is devoted to the theory of two-dimensional Riemannian manifolds of bounded curvature.Concepts of Riemannian geometry such as the area and integral curvature of a set and the length and integral curvature of a curve are also defined for these manifolds.Some fundamental results of Riemannian geometry.

In particular, he introduced the class of two-dimensional manifolds of bounded curvature. They exhaust the class of all metrized two-dimensional manifolds that admit, in a neighborhood of each point, a uniform approximation by Riemannian metrics with absolute integral curvature (i.e., the integral of the module of Gaussian curvature) bounded in.

§ 8. Spaces of curvature Chapter III. The space of directions § 9. The space of directions at a point in § The tangent space Chapter IV. Spaces of bounded curvature § Spaces of curvature both and § Introduction of the Riemannian structure Chapter V.

Smoothness of the metric in spaces of bounded curvature § Parallel translationCited by: The book contains a survey of research on non-regular Riemannian geome­ try, carried out mainly by Soviet authors. The beginning of this direction oc­ curred in the works of A. Aleksandrov on the intrinsic geometry of convex surfaces.

In this paper we investigate the "area blow-up" set of a sequence of smooth co-dimension one manifolds whose first variation with respect to an anisotropic integral is bounded.

Following the ideas introduced by White in [12], we show that this set has bounded (anisotropic) mean curvature in the viscosity by: 2.

of spaces other than Riemannian manifolds whose curvature is bounded above. An interesting class of non-positively curved polyhedral complexes is provided by the buildings of Euclidean (or affine) type which arose in the work of Bruhat and Tits on algebraic groups.

Many other examples will be described in the course of this book. Introduction to differentiable manifolds Lecture notes versionNovember 5, This is a self contained set of lecture notes.

The notes were written by Rob van der Vorst. The solution manual is written by Guit-Jan Ridderbos. We follow the book ‘Introduction to Smooth Manifolds’ by John M. Lee as a reference text [1].

Since two dimensional Cartan–Hadamard manifolds with the sectional curvature satisfying Sec ≥ − κ such that κ ∈ R + only involve in this study, the model space to be considered here should be a two dimensional hyperbolic space H κ as the one which we have used in the Cheeger–Yau bound in search of a lower estimate for the on Author: Burak Tevfik Kaynak, O.

Teoman Turgut. [17] Yurii G. Reshetnyak. Two-dimensional manifolds of bounded curvature. In Geometry, IV, volume 70 of Encyclopaedia Math.

Sci., pagesSpringer, Berlin, [18] Karl-Theodor Sturm. Ricci Tensor for Diffusion Operators and Curvature-Dimension Inequalities under Conformal Transformations and Time Changes. Preprint arXiv File Size: KB. In differential geometry, the Ricci flow (/ ˈ r iː tʃ i /, Italian:) is an intrinsic geometric is a process that deforms the metric of a Riemannian manifold in a way formally analogous to the diffusion of heat.

Heuristically speaking, at every point of the manifold the Ricci flow shrinks directions of positive curvature and expands directions of negative curvature, while. The curvature is a quantity describing how the geometry of a space differs locally from the one of the flat curvature of any locally isotropic space (and hence of a locally isotropic universe) falls into one of the three following cases.

Zero curvature (flat); a drawn triangle's angles add up to ° and the Pythagorean theorem holds; such 3-dimensional space is locally modeled by. We show that the negative Gauss curvature of the ambient surface gives rise to a Hardy inequality and use this to prove certain stability of spec-trum in the case of asymptotically straight strips about mildly perturbed geodesics.

1 Introduction Problems linking the geometry of .The local isometric embedding in R^3 of two-dimensional Riemannian manifolds with Gaussian curvature changing sign to finite order on a curve: Watson, Oliver: (C.L. Chai) Equicharacteristic Tate conjecture for Drinfeld modules: Yin, Cui: (D.

Harbater) The mapping class group and special Loci in moduli of curves: Atria, Matias: (T.() Subgradient Projection Algorithms for Convex Feasibility on Riemannian Manifolds with Lower Bounded Curvatures. Journal of Optimization Theory and Applications() Concepts and techniques of optimization on the by: