Topic
Global analysis
About: Global analysis is a research topic. Over the lifetime, 780 publications have been published within this topic receiving 36894 citations. The topic is also known as: analysis on manifolds.
Papers published on a yearly basis
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Papers
Book•
30 Sep 1997TL;DR: Calculus of smooth mappings Calculus of holomorphic and real analytic mappings Partitions of unity Smoothly real compact spaces Extensions and liftings of mappings Infinite dimensional manifolds Calculus on infinite dimensional manifold, infinite dimensional differential geometry Manifolds of Mappings Further applications References as mentioned in this paper.
Abstract: Introduction Calculus of smooth mappings Calculus of holomorphic and real analytic mappings Partitions of unity Smoothly realcompact spaces Extensions and liftings of mappings Infinite dimensional manifolds Calculus on infinite dimensional manifolds Infinite dimensional differential geometry Manifolds of mappings Further applications References Index.
1,499 citations
Book•
1 Jan 1977
TL;DR: In this paper, a review of fundamental notions of analysis is presented, including differential calculus on Banach spaces, integration on manifolds, and connection on a principle fibre bundle. But the authors do not consider the infinite dimensional case of manifolds.
Abstract: Preface. Chapters: I. Review of fundamental notions of analysis. II. Differential calculus on Banach spaces. III. Differentiable manifolds, finite dimensional case. IV. Integration on manifolds. V. Riemannian manifolds. Kahlerian manifolds. V bis. Connections on a principle fibre bundle. VI. Distributions. VII. Differentiable manifolds, infinite dimensional case. References. Symbols. Index.
1,079 citations
Book•
1 Jan 1999TL;DR: In the non-compact setting Euclidean-type Sobolev inequalities with constraints were defined in this article, where the optimal constants in the compact setting were defined by Euclideans.
Abstract: Elements of Riemannian geometry Sobolev spaces: The compact setting Sobolev spaces: The noncompact setting Best constants in the compact setting I Best constants in the compact setting II Optimal inequalities with constraints Best constants in the noncompact setting Euclidean-type Sobolev inequalities The influence of symmetries Manifolds with boundary Bibliography.
1,042 citations
Book•
1 Oct 1964TL;DR: Manifolds Lie groups Fibre bundles Differential forms Connexions Affine connexions Riemannian manifolds Geodesics and complete RiemANNian manifoldolds Riemmannian curvature Immersions and the second fundamental form Second variation of arc length Theorems on differential equations Bibliography Subject index as mentioned in this paper
Abstract: Manifolds Lie groups Fibre bundles Differential forms Connexions Affine connexions Riemannian manifolds Geodesics and complete Riemannian manifolds Riemannian curvature Immersions and the second fundamental form Second variation of arc length Theorems on differential equations Bibliography Subject index.
974 citations
TL;DR: In this article, the concept of an inertial manifold for nonlinear evolutionary equations, in particular for ordinary and partial differential equations, was introduced, which is an appropriate tool for the study of questions related to the long time behavior of solutions of the evolutionary equations.
782 citations
Related Topics (5)
Performance Metrics
| Year | Papers |
|---|---|
| 2022 | 1 |
| 2021 | 4 |
| 2020 | 3 |
| 2019 | 5 |
| 2018 | 3 |
| 2017 | 22 |