Introduction to Global Analysis – Minimal Surfaces in Riemannian Manifolds Moore

Introduction to Global AnalysisMinimal Surfaces in Riemannian Manifolds\nAuthor(s): John Douglas Moore\nFormat: Hardback\nPublisher: American Mathematical Society, United States\nImprint: American Mathematical Society\nISBN-13: 9781470429508, 978-1470429508\nSynopsis\nDuring the last century, global analysis was one of the main sources of interaction between geometry and topology. One might argue that the core of this subject is Morse theory, according to which the critical points of a generic smooth proper function on a manifold $M$ determine the homology of the manifold.\n\nMorse envisioned applying this idea to the calculus of variations, including the theory of periodic motion in classical mechanics, by approximating the space of loops on $M$ by a finite-dimensional manifold of high dimension. Palais and Smale reformulated Morse's calculus of variations in terms of infinite-dimensional manifolds, and these infinite-dimensional manifolds were found useful for studying a wide varie.