A Poincaré Formula for Differential Forms and Applications
We prove a new general Poincaré-type inequality for differential forms on compact Riemannian manifolds with nonempty boundary. When the boundary is isometrically immersed in Euclidean space, we derive a new inequality involving mean and scalar curvatures of the boundary only and characterize its lim...
Збережено в:
| Опубліковано в: : | Symmetry, Integrability and Geometry: Methods and Applications |
|---|---|
| Дата: | 2023 |
| Автори: | , , |
| Формат: | Стаття |
| Мова: | Англійська |
| Опубліковано: |
Інститут математики НАН України
2023
|
| Онлайн доступ: | https://nasplib.isofts.kiev.ua/handle/123456789/212043 |
| Теги: |
Додати тег
Немає тегів, Будьте першим, хто поставить тег для цього запису!
|
| Назва журналу: | Digital Library of Periodicals of National Academy of Sciences of Ukraine |
| Цитувати: | A Poincaré Formula for Differential Forms and Applications. Nicolas Ginoux, Georges Habib and Simon Raulot. SIGMA 19 (2023), 088, 17 pages |
Репозитарії
Digital Library of Periodicals of National Academy of Sciences of Ukraine| _version_ | 1862707017132539904 |
|---|---|
| author | Ginoux, Nicolas Habib, Georges Raulot, Simon |
| author_facet | Ginoux, Nicolas Habib, Georges Raulot, Simon |
| citation_txt | A Poincaré Formula for Differential Forms and Applications. Nicolas Ginoux, Georges Habib and Simon Raulot. SIGMA 19 (2023), 088, 17 pages |
| collection | DSpace DC |
| container_title | Symmetry, Integrability and Geometry: Methods and Applications |
| description | We prove a new general Poincaré-type inequality for differential forms on compact Riemannian manifolds with nonempty boundary. When the boundary is isometrically immersed in Euclidean space, we derive a new inequality involving mean and scalar curvatures of the boundary only and characterize its limiting case in codimension one. A new Ros-type inequality for differential forms is also derived, assuming the existence of a nonzero parallel form on the manifold.
|
| first_indexed | 2026-03-19T03:06:23Z |
| format | Article |
| fulltext | |
| id | nasplib_isofts_kiev_ua-123456789-212043 |
| institution | Digital Library of Periodicals of National Academy of Sciences of Ukraine |
| issn | 1815-0659 |
| language | English |
| last_indexed | 2026-03-19T03:06:23Z |
| publishDate | 2023 |
| publisher | Інститут математики НАН України |
| record_format | dspace |
| spelling | Ginoux, Nicolas Habib, Georges Raulot, Simon 2026-01-23T10:11:26Z 2023 A Poincaré Formula for Differential Forms and Applications. Nicolas Ginoux, Georges Habib and Simon Raulot. SIGMA 19 (2023), 088, 17 pages 1815-0659 2020 Mathematics Subject Classification: 53C21; 53C24; 58J32; 58J50 arXiv:2307.03616 https://nasplib.isofts.kiev.ua/handle/123456789/212043 https://doi.org/10.3842/SIGMA.2023.088 We prove a new general Poincaré-type inequality for differential forms on compact Riemannian manifolds with nonempty boundary. When the boundary is isometrically immersed in Euclidean space, we derive a new inequality involving mean and scalar curvatures of the boundary only and characterize its limiting case in codimension one. A new Ros-type inequality for differential forms is also derived, assuming the existence of a nonzero parallel form on the manifold. We are very grateful to the Mathematisches Forschungsinstitut Oberwolfach (MFO) and the Centre International de Rencontres Mathématiques (CIRM, Luminy), where most of the work was carried out. The second-named author also thanks the Alfried Krupp Wissenschaftskolleg for its support. Last but not least, we are grateful to the referees for their constructive comments. en Інститут математики НАН України Symmetry, Integrability and Geometry: Methods and Applications A Poincaré Formula for Differential Forms and Applications Article published earlier |
| spellingShingle | A Poincaré Formula for Differential Forms and Applications Ginoux, Nicolas Habib, Georges Raulot, Simon |
| title | A Poincaré Formula for Differential Forms and Applications |
| title_full | A Poincaré Formula for Differential Forms and Applications |
| title_fullStr | A Poincaré Formula for Differential Forms and Applications |
| title_full_unstemmed | A Poincaré Formula for Differential Forms and Applications |
| title_short | A Poincaré Formula for Differential Forms and Applications |
| title_sort | poincaré formula for differential forms and applications |
| url | https://nasplib.isofts.kiev.ua/handle/123456789/212043 |
| work_keys_str_mv | AT ginouxnicolas apoincareformulafordifferentialformsandapplications AT habibgeorges apoincareformulafordifferentialformsandapplications AT raulotsimon apoincareformulafordifferentialformsandapplications AT ginouxnicolas poincareformulafordifferentialformsandapplications AT habibgeorges poincareformulafordifferentialformsandapplications AT raulotsimon poincareformulafordifferentialformsandapplications |