Accession Number:

ADA141748

Title:

On the Scattering of Electromagnetic Waves by Perfectly Conducting Bodies Moving in Vacuum. Part 6. Manifolds in Euclidean Spaces, Regularity Properties of Domains.

Descriptive Note:

Final technical rept.,

Corporate Author:

DELAWARE UNIV NEWARK APPLIED MATHEMATICS INST

Personal Author(s):

Report Date:

1984-04-01

Pagination or Media Count:

190.0

Abstract:

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

Subject Categories:

  • Theoretical Mathematics
  • Electricity and Magnetism
  • Optics

Distribution Statement:

APPROVED FOR PUBLIC RELEASE