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.
"synopsis" may belong to another edition of this title.
Shipping:
£ 3.38
Within U.S.A.
Seller: Zubal-Books, Since 1961, Cleveland, OH, U.S.A.
Condition: Good. 154 pp., paperback, ex library, else text clean & binding tight. - If you are reading this, this item is actually (physically) in our stock and ready for shipment once ordered. We are not bookjackers. Buyer is responsible for any additional duties, taxes, or fees required by recipient's country. Seller Inventory # ZB1277092
Quantity: 1 available
Seller: Michener & Rutledge Booksellers, Inc., Baldwin City, KS, U.S.A.
Paperback. Condition: Very Good. Paper yellowing, otherwise text clean and solid ; Oberwolfach Seminars; 0 X 0 X 0 inches; 153 pages. Seller Inventory # 205121
Quantity: 1 available
Seller: Moe's Books, Berkeley, CA, U.S.A.
Soft cover. Condition: Good. No jacket. Spine is sunned. Cover is worn, especially along edges. Bottom front cover corner is slightly folded. Inside is tanned and lightly foxed, but legibility is not affected. Seller Inventory # 1142268
Quantity: 1 available