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Critical Point Theory and Submanifold Geometry (Lecture Notes in Mathematics / Nankai Institute of Mathematics, Tianjin, P.R. China)
Critical Point Theory and Submanifold Geometry (Lecture Notes in Mathematics / Nankai Institute of Mathematics, Tianjin, P.R. China)
Date: 21 June 2011, 01:29
This book is divided into two parts. Part I is a modern introduction to the very classical theory of submanifold geometry. We go beyond the classical theory in at least one important respect; we study submanifolds of Hilbert space as well as of Euclidean spaces. Part II is devoted to critical point theory, and here again the theory is developed in the setting of Hilbert manifolds. The two parts are inter-related through the Morse Index Theorem, that is, the fact that the structure of the set of critical points of the distance function from a point to a submanifold can be described completely in terms of the local geometric invariants of the submanifold.

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