About: Weyl's tube formula

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Weyl's tube formula gives the volume of an object defined as the set of all points within a small distance of a manifold. Let be an oriented, closed, two-dimensional surface, and let denote the set of all points within a distance of the surface . Then, for sufficiently small, the volume of is where is the area of the surface and is its Euler characteristic. This expression can be generalized to the case where is a -dimensional submanifold of -dimensional Euclidean space .

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  • Weyl's tube formula gives the volume of an object defined as the set of all points within a small distance of a manifold. Let be an oriented, closed, two-dimensional surface, and let denote the set of all points within a distance of the surface . Then, for sufficiently small, the volume of is where is the area of the surface and is its Euler characteristic. This expression can be generalized to the case where is a -dimensional submanifold of -dimensional Euclidean space . (en)
  • Формула трубки или формула Вейля — выражение для объёма -окрестности подмногообразия как многочлен от . Предложена Германом Вейлем. (ru)
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  • Weyl's tube formula gives the volume of an object defined as the set of all points within a small distance of a manifold. Let be an oriented, closed, two-dimensional surface, and let denote the set of all points within a distance of the surface . Then, for sufficiently small, the volume of is where is the area of the surface and is its Euler characteristic. This expression can be generalized to the case where is a -dimensional submanifold of -dimensional Euclidean space . (en)
  • Формула трубки или формула Вейля — выражение для объёма -окрестности подмногообразия как многочлен от . Предложена Германом Вейлем. (ru)
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  • Формула трубки (ru)
  • Weyl's tube formula (en)
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