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首页> 美国政府科技报告 >Scattering of Electromagnetic Waves by Perfectly Conducting Bodies Moving in Vacuum. Part 6. Manifolds in Euclidean Spaces, Regularity Properties of Domains
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Scattering of Electromagnetic Waves by Perfectly Conducting Bodies Moving in Vacuum. Part 6. Manifolds in Euclidean Spaces, Regularity Properties of Domains

机译：真空中完全导体的电磁波散射。第6部分欧几里德空间中的流形，域的正则性

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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)

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