Mass from an Extrinsic Point of View
We express the -th Gauss-Bonnet-Chern mass of an immersed submanifold of Euclidean space as a linear combination of two terms: the total (2)-th mean curvature and the integral, over the entire manifold, of the inner product between the (2 + 1)-th mean curvature vector and the position vector of the...
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| Veröffentlicht in: | Symmetry, Integrability and Geometry: Methods and Applications |
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| Datum: | 2025 |
| Hauptverfasser: | , |
| Format: | Artikel |
| Sprache: | Englisch |
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Інститут математики НАН України
2025
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| Online Zugang: | https://nasplib.isofts.kiev.ua/handle/123456789/212873 |
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| Назва журналу: | Digital Library of Periodicals of National Academy of Sciences of Ukraine |
| Zitieren: | Mass from an Extrinsic Point of View. Alexandre de Sousa and Frederico Girão. SIGMA 21 (2025), 018, 11 pages |
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Digital Library of Periodicals of National Academy of Sciences of Ukraine| _version_ | 1862579788053479424 |
|---|---|
| author | de Sousa, Alexandre Girão, Frederico |
| author_facet | de Sousa, Alexandre Girão, Frederico |
| citation_txt | Mass from an Extrinsic Point of View. Alexandre de Sousa and Frederico Girão. SIGMA 21 (2025), 018, 11 pages |
| collection | DSpace DC |
| container_title | Symmetry, Integrability and Geometry: Methods and Applications |
| description | We express the -th Gauss-Bonnet-Chern mass of an immersed submanifold of Euclidean space as a linear combination of two terms: the total (2)-th mean curvature and the integral, over the entire manifold, of the inner product between the (2 + 1)-th mean curvature vector and the position vector of the immersion. As a consequence, we obtain, for each , a geometric inequality that holds whenever the positive mass theorem (for the -th Gauss-Bonnet-Chern mass) holds.
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| first_indexed | 2026-03-21T11:56:48Z |
| format | Article |
| fulltext | |
| id | nasplib_isofts_kiev_ua-123456789-212873 |
| institution | Digital Library of Periodicals of National Academy of Sciences of Ukraine |
| issn | 1815-0659 |
| language | English |
| last_indexed | 2026-03-21T11:56:48Z |
| publishDate | 2025 |
| publisher | Інститут математики НАН України |
| record_format | dspace |
| spelling | de Sousa, Alexandre Girão, Frederico 2026-02-13T13:49:03Z 2025 Mass from an Extrinsic Point of View. Alexandre de Sousa and Frederico Girão. SIGMA 21 (2025), 018, 11 pages 1815-0659 2020 Mathematics Subject Classification: 83C99; 53C40; 51M16 arXiv:2403.06782 https://nasplib.isofts.kiev.ua/handle/123456789/212873 https://doi.org/10.3842/SIGMA.2025.018 We express the -th Gauss-Bonnet-Chern mass of an immersed submanifold of Euclidean space as a linear combination of two terms: the total (2)-th mean curvature and the integral, over the entire manifold, of the inner product between the (2 + 1)-th mean curvature vector and the position vector of the immersion. As a consequence, we obtain, for each , a geometric inequality that holds whenever the positive mass theorem (for the -th Gauss-Bonnet-Chern mass) holds. This study was partially financed by the Coordenação de Aperfeiçoamento de Pessoal de Nível Superior- Brasil (CAPES) - Finance Code 001. This work was partially done while Alexandre de Sousa was a CAPES Fellow at the Mathematics Institute of Federal University of Alagoas (IM/UFAL), whose members he would like to thank for the hospitality. Frederico Girão was partially supported by CNPq, grant number 307239/2020-9. en Інститут математики НАН України Symmetry, Integrability and Geometry: Methods and Applications Mass from an Extrinsic Point of View Article published earlier |
| spellingShingle | Mass from an Extrinsic Point of View de Sousa, Alexandre Girão, Frederico |
| title | Mass from an Extrinsic Point of View |
| title_full | Mass from an Extrinsic Point of View |
| title_fullStr | Mass from an Extrinsic Point of View |
| title_full_unstemmed | Mass from an Extrinsic Point of View |
| title_short | Mass from an Extrinsic Point of View |
| title_sort | mass from an extrinsic point of view |
| url | https://nasplib.isofts.kiev.ua/handle/123456789/212873 |
| work_keys_str_mv | AT desousaalexandre massfromanextrinsicpointofview AT giraofrederico massfromanextrinsicpointofview |