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Convex Functions and Optimization Methods on Riemannian Manifolds
The object of this book is to present the basic facts of convex functions, standard dynamical systems, descent numerical algorithms and some computer programs on Riemannian manifolds in a form suitable for applied mathematicians, scientists and engineers. It contains mathematical information on these subjects and applications distributed in seven chapters whose topics are close to my own areas of research: Metric properties of Riemannian manifolds, First and second variations of the p-energy of a curve; Convex functions on Riemannian manifolds; Geometric examples of convex functions; Flows, convexity and energies; Semidefinite Hessians and applications; Minimization of functions on Riemannia...
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Spectral Theory of Differential Operators
Spectral Theory of Differential Operators
Geometry of Harmonic Maps
Harmonic maps are solutions to a natural geometrical variational prob lem. This notion grew out of essential notions in differential geometry, such as geodesics, minimal surfaces and harmonic functions. Harmonic maps are also closely related to holomorphic maps in several complex variables, to the theory of stochastic processes, to nonlinear field theory in theoretical physics, and to the theory of liquid crystals in materials science. During the past thirty years this subject has been developed extensively. The monograph is by no means intended to give a complete description of the theory of harmonic maps. For example, the book excludes a large part of the theory of harmonic maps from 2-dim...
Plasticity in Sensory Systems
This broad exploration of research in plasticity in sensory systems focuses on visual and auditory systems. Topics include visual and visuomotor learning, sensory adaptations as a result of visual loss in childhood, plasticity in the adult visual system, plasticity across the senses, and new techniques in vision recovery, rehabilitation, and sensory substitution.
