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Differential Geometry: Connections, Curvature, and Characteristic Classes (Graduate Texts in Mathematics) | Lectures on the H-cobordism Theorem | Algebraic Topology | Mathematical Methods of Classical Mechanics | Elliptic Partial Differential Equations of Second Order | Confoliations | Differential Topology
The authors cover two main methods for proving the $h$-principle: holonomic approximation and convex integration. The reader will find that, with a few notable exceptions, most instances of the $h$-principle can be treated by the methods considered here. A special emphasis in the book is made on applications to symplectic and contact geometry.
Gromov's famous book "Partial Differential Relations", which is devoted to the same subject, is an encyclopedia of the $h$-principle, written for experts, while the present book is the first broadly accessible exposition of the theory and its applications. The book would be an excellent text for a graduate course on geometric methods for solving partial differential equations and inequalities. Geometers, topologists and analysts will also find much value in this very readable exposition of an important and remarkable topic.
About: In differential geometry and topology one often deals with systems of partial differential equations, as well as partial differential inequalities, that have infinitely many solutions whatever boundary conditions are imposed.
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