Geometric Mechanics on Riemannian Manifolds Applications to Partial Differential Equations /

• Main Authors: Calin, Ovidiu (Author), Chang, Der-Chen (Author)
• Corporate Author: SpringerLink (Online service)
• Format: Electronic eBook
• Language: English
• Published: Boston, MA : Birkhäuser Boston, 2005.
• Series: Applied and Numerical Harmonic Analysis
• Subjects: Mathematics.; Harmonic analysis.; Fourier analysis.; Partial differential equations.; Applied mathematics.; Engineering mathematics.; Differential geometry.; Physics.; Fourier Analysis.; Differential Geometry.; Partial Differential Equations.; Mathematical Methods in Physics.; Abstract Harmonic Analysis.; Applications of Mathematics.

Differential geometry techniques have very useful and important applications in partial differential equations and quantum mechanics. This work presents a purely geometric treatment of problems in physics involving quantum harmonic oscillators, quartic oscillators, minimal surfaces, and Schrödinger&...

Table of Contents:

• Introductory Chapter
• Laplace Operators on Riemannian Manifolds
• Lagrangian Formalism on Riemannian Manifolds
• Harmonic Maps from a Lagrangian Viewpoint
• Conservation Theorems
• Hamiltonian Formalism
• Hamilton-Jacobi Theory
• Minimal Hypersurfaces
• Radially Symmetric Spaces
• Fundamental Solutions for Heat Operators with Potentials
• Fundamental Solutions for Elliptic Operators
• Mechanical Curves.