On the Scattering of Electromagnetic Waves by Perfectly Conducting Bodies Moving in Vacuum. Part 6. Manifolds in Euclidean Spaces, Regularity Properties of Domains.
Final technical rept.,
DELAWARE UNIV NEWARK APPLIED MATHEMATICS INST
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Various standard results concerning manifolds in euclidean spaces, coordinate systems, and functions defined on such manifolds are developed and organized. For example, conditions are identified under which the image of a manifold is again a manifold. A development of Lebesgue measure and integration on a manifold is presented. Included is a change-of-variables formula for the transformation of an integral over a manifold to integration over a second manifold suitably related to the first. Classes of regular domains are defined. Special attention is given to those regular domains possessing a Holder-continuous exterior unit normal field, or Lyapunov domains. Slightly modifying the standard presentations, geometric and analytic properties of the boundary of a Lyapunov domain are derived, including the identification of certain canonical tangent-plane coordinate systems. Author
- Theoretical Mathematics
- Electricity and Magnetism