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＜電子ブック＞
Nonlinear Methods in Riemannian and Kählerian Geometry : Delivered at the German Mathematical Society Seminar in Düsseldorf in June, 1986 / by Jürgen Jost

版	2nd ed. 1991.
出版者	Basel : Birkhäuser Basel : Imprint: Birkhäuser
出版年	1991
本文言語	英語
大きさ	156 p : online resource
冊子体	Nonlinear methods in Riemannian and Kahlerian geometry / Jurgen Jost ; 10
著者標目	*Jost, Jürgen author SpringerLink (Online service)
件　名	LCSH:Geometry FREE:Geometry
一般注記	1. Geometric preliminaries -- 2. Some principles of analysis -- 3. The heat flow on manifolds. Existence and uniqueness of harmonic maps into nonpositively curved image manifolds -- 4. The parabolic Yang-Mills equation -- 5. Geometric applications of harmonic maps -- Appendix: Some remarks on notation and terminology In this book, I present an expanded version of the contents of my lectures at a Seminar of the DMV (Deutsche Mathematiker Vereinigung) in Düsseldorf, June, 1986. The title "Nonlinear methods in complex geometry" already indicates a combination of techniques from nonlinear partial differential equations and geometric concepts. In older geometric investigations, usually the local aspects attracted more attention than the global ones as differential geometry in its foundations provides approximations of local phenomena through infinitesimal or differential constructions. Here, all equations are linear. If one wants to consider global aspects, however, usually the presence of curvature Ieads to a nonlinearity in the equations. The simplest case is the one of geodesics which are described by a system of second ordernonlinear ODE; their linearizations are the Jacobi fields. More recently, nonlinear PDE played a more and more pro~inent röle in geometry. Let us Iist some of the most important ones: - harmonic maps between Riemannian and Kählerian manifolds - minimal surfaces in Riemannian manifolds - Monge-Ampere equations on Kähler manifolds - Yang-Mills equations in vector bundles over manifolds. While the solution of these equations usually is nontrivial, it can Iead to very signifi­ cant results in geometry, as solutions provide maps, submanifolds, metrics, or connections which are distinguished by geometric properties in a given context. All these equations are elliptic, but often parabolic equations are used as an auxiliary tool to solve the elliptic ones Accessibility summary: This PDF is not accessible. It is based on scanned pages and does not support features such as screen reader compatibility or described non-text content (images, graphs etc). However, it likely supports searchable and selectable text based on OCR (Optical Character Recognition). Users with accessibility needs may not be able to use this content effectively. Please contact us at accessibilitysupport@springernature.com if you require assistance or an alternative format Inaccessible, or known limited accessibility No reading system accessibility options actively disabled Publisher contact for further accessibility information: accessibilitysupport@springernature.com HTTP:URL=https://doi.org/10.1007/978-3-0348-7706-0

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