Some Integral Formulas for the (r + 1)th Mean Curvature of a Closed Hypersurface
By using the operator 𝐿𝑟, we define the notions of rth order and rth type of a Euclidean hypersurface. By the use of these notions, we are able to obtain some sharp estimates of the (𝑟+1)th mean curvature for a closed hypersurface of the Euclidean space in terms of rth order.
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| Main Authors: | , |
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| Format: | Article |
| Language: | English |
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Wiley
2012-01-01
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| Series: | International Journal of Mathematics and Mathematical Sciences |
| Online Access: | http://dx.doi.org/10.1155/2012/784028 |
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| author | Akram Mohammadpouri S. M. B. Kashani |
| author_facet | Akram Mohammadpouri S. M. B. Kashani |
| author_sort | Akram Mohammadpouri |
| collection | DOAJ |
| description | By using the operator 𝐿𝑟, we define the notions of rth order and rth type of a Euclidean hypersurface. By the use of these notions, we are able to obtain some sharp estimates of the (𝑟+1)th mean curvature for a closed hypersurface of the Euclidean space in terms of rth order. |
| format | Article |
| id | doaj-art-782a471fcb5b4f0ca971e367ca74554e |
| institution | Kabale University |
| issn | 0161-1712 1687-0425 |
| language | English |
| publishDate | 2012-01-01 |
| publisher | Wiley |
| record_format | Article |
| series | International Journal of Mathematics and Mathematical Sciences |
| spelling | doaj-art-782a471fcb5b4f0ca971e367ca74554e2025-08-20T03:35:11ZengWileyInternational Journal of Mathematics and Mathematical Sciences0161-17121687-04252012-01-01201210.1155/2012/784028784028Some Integral Formulas for the (r + 1)th Mean Curvature of a Closed HypersurfaceAkram Mohammadpouri0S. M. B. Kashani1Department of Pure Mathematics, Faculty of Mathematical Sciences, Tarbiat Modares University, P.O. Box 14115-134, Tehran, IranDepartment of Pure Mathematics, Faculty of Mathematical Sciences, Tarbiat Modares University, P.O. Box 14115-134, Tehran, IranBy using the operator 𝐿𝑟, we define the notions of rth order and rth type of a Euclidean hypersurface. By the use of these notions, we are able to obtain some sharp estimates of the (𝑟+1)th mean curvature for a closed hypersurface of the Euclidean space in terms of rth order.http://dx.doi.org/10.1155/2012/784028 |
| spellingShingle | Akram Mohammadpouri S. M. B. Kashani Some Integral Formulas for the (r + 1)th Mean Curvature of a Closed Hypersurface International Journal of Mathematics and Mathematical Sciences |
| title | Some Integral Formulas for the (r + 1)th Mean Curvature of a Closed Hypersurface |
| title_full | Some Integral Formulas for the (r + 1)th Mean Curvature of a Closed Hypersurface |
| title_fullStr | Some Integral Formulas for the (r + 1)th Mean Curvature of a Closed Hypersurface |
| title_full_unstemmed | Some Integral Formulas for the (r + 1)th Mean Curvature of a Closed Hypersurface |
| title_short | Some Integral Formulas for the (r + 1)th Mean Curvature of a Closed Hypersurface |
| title_sort | some integral formulas for the r 1 th mean curvature of a closed hypersurface |
| url | http://dx.doi.org/10.1155/2012/784028 |
| work_keys_str_mv | AT akrammohammadpouri someintegralformulasforther1thmeancurvatureofaclosedhypersurface AT smbkashani someintegralformulasforther1thmeancurvatureofaclosedhypersurface |