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In differential geometry, Cohn-Vossen's inequality, named after Stefan Cohn-Vossen, relates the integral of Gaussian curvature of a non-compact surface to the Euler characteristic. It is akin to the Gauss–Bonnet theorem for a compact surface. where K is the Gaussian curvature, dA is the element of area, and χ is the Euler characteristic.

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  • Cohn-Vossen's inequality (en)
  • Неравенство Кон-Фоссена (ru)
  • Нерівність Кон-Фоссена (uk)
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  • Неравенство Кон-Фоссена связывает интеграл от гауссовой кривизны некомпактной поверхности с её эйлеровой характеристикой.Это неравенство аналогично формуле Гаусса — Бонне. Названо в честь Стефана Эммануиловича Кон-Фоссена. (ru)
  • Нерівність Кон-Фоссена пов'язує інтеграл від гаусової кривини некомпактної поверхні з її ейлеровою характеристикою. Ця нерівність аналогічна формулі Гаусса — Бонне. Названа на честь Стефана Емануїловича Кон-Фоссена. (uk)
  • In differential geometry, Cohn-Vossen's inequality, named after Stefan Cohn-Vossen, relates the integral of Gaussian curvature of a non-compact surface to the Euler characteristic. It is akin to the Gauss–Bonnet theorem for a compact surface. where K is the Gaussian curvature, dA is the element of area, and χ is the Euler characteristic. (en)
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  • In differential geometry, Cohn-Vossen's inequality, named after Stefan Cohn-Vossen, relates the integral of Gaussian curvature of a non-compact surface to the Euler characteristic. It is akin to the Gauss–Bonnet theorem for a compact surface. A divergent path within a Riemannian manifold is a smooth curve in the manifold that is not contained within any compact subset of the manifold. A complete manifold is one in which every divergent path has infinite length with respect to the Riemannian metric on the manifold. Cohn-Vossen's inequality states that in every complete Riemannian 2-manifold S with finite total curvature and finite Euler characteristic, we have where K is the Gaussian curvature, dA is the element of area, and χ is the Euler characteristic. (en)
  • Неравенство Кон-Фоссена связывает интеграл от гауссовой кривизны некомпактной поверхности с её эйлеровой характеристикой.Это неравенство аналогично формуле Гаусса — Бонне. Названо в честь Стефана Эммануиловича Кон-Фоссена. (ru)
  • Нерівність Кон-Фоссена пов'язує інтеграл від гаусової кривини некомпактної поверхні з її ейлеровою характеристикою. Ця нерівність аналогічна формулі Гаусса — Бонне. Названа на честь Стефана Емануїловича Кон-Фоссена. (uk)
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