Morse Theory Of Gradient Flows, Concavity And Complexity On Manifolds With Boundary
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A01=Gabriel Katz
Author_Gabriel Katz
Boundary Effects
Category=PBMW
Category=PBPD
Complexity
Convexity
eq_isMigrated=1
eq_isMigrated=2
eq_nobargain
Gradient Flows
Morse Theory
Product details
- ISBN 9789814368759
- Publication Date: 30 Aug 2019
- Publisher: World Scientific Publishing Co Pte Ltd
- Publication City/Country: SG
- Product Form: Hardback
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This monograph is an account of the author's investigations of gradient vector flows on compact manifolds with boundary. Many mathematical structures and constructions in the book fit comfortably in the framework of Morse Theory and, more generally, of the Singularity Theory of smooth maps.The geometric and combinatorial structures, arising from the interactions of vector flows with the boundary of the manifold, are surprisingly rich. This geometric setting leads organically to many encounters with Singularity Theory, Combinatorics, Differential Topology, Differential Geometry, Dynamical Systems, and especially with the boundary value problems for ordinary differential equations. This diversity of connections animates the book and is the main motivation behind it.The book is divided into two parts. The first part describes the flows in three dimensions. It is more pictorial in nature. The second part deals with the multi-dimensional flows, and thus is more analytical. Each of the nine chapters starts with a description of its purpose and main results. This organization provides the reader with independent entrances into different chapters.
