Metric Lie Groups
This Open Access textbook presents Carnot-Carathéodory spaces from the perspective of Lie groups. Its main objective is to illustrate how these non-smooth geometries manifest in various mathematical domains, including metric geometry and geometric group theory. In contrast to other sources, this boo...
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| Үндсэн зохиолч: | |
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| Формат: | Online |
| Хэл сонгох: | англи |
| Хэвлэсэн: |
Springer Nature
2025
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| Нөхцлүүд: | |
| Онлайн хандалт: | ONIX_20251020T130859_9783031988325_51 |
| Шошгууд: |
Шошго байхгүй, Энэхүү баримтыг шошголох эхний хүн болох!
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| _version_ | 1869527893491580928 |
|---|---|
| author | Le Donne, Enrico |
| author_browse | Le Donne, Enrico |
| author_facet | Le Donne, Enrico |
| author_sort | Le Donne, Enrico |
| collection | Directory of Open Access Books |
| description | This Open Access textbook presents Carnot-Carathéodory spaces from the perspective of Lie groups. Its main objective is to illustrate how these non-smooth geometries manifest in various mathematical domains, including metric geometry and geometric group theory. In contrast to other sources, this book utilizes the formalism of Lie groups to showcase how this theory facilitates the development of geometry and analysis on the non-smooth structure of Carnot-Carathéodory spaces. Major results are presented with rigorous mathematical proofs, and references for further exploration are provided. Open problems in these areas are discussed, offering insights into recent developments and avenues for future research. Prerequisite topics such as differential geometry, measure theory, and group theory are incorporated in the main flow of the chapters, ensuring a comprehensive understanding. Junior researchers seeking an introduction to the field of sub-Riemannian geometry will find this an invaluable introductory companion. The book is also suitable for those entering research subjects on the interplay between geometry, analysis, and group theory. |
| format | Online |
| id | doab-20.500.12854ir-168406 |
| institution | Directory of Open Access Books |
| language | eng |
| publishDate | 2025 |
| publishDateRange | 2025 |
| publishDateSort | 2025 |
| publisher | Springer Nature |
| publisherStr | Springer Nature |
| record_format | ojs |
| spelling | doab-20.500.12854ir-1684062025-10-21T05:22:52Z Metric Lie Groups Le Donne, Enrico Open Access Carnot-Carathéodory Space Nilpotent Lie Group Sub-Riemannian Geometry Sub-Finsler Geometry Heisenberg Group Heintze Group Pansu Theorem thema EDItEUR::P Mathematics and Science::PB Mathematics::PBM Geometry::PBMP Differential and Riemannian geometry This Open Access textbook presents Carnot-Carathéodory spaces from the perspective of Lie groups. Its main objective is to illustrate how these non-smooth geometries manifest in various mathematical domains, including metric geometry and geometric group theory. In contrast to other sources, this book utilizes the formalism of Lie groups to showcase how this theory facilitates the development of geometry and analysis on the non-smooth structure of Carnot-Carathéodory spaces. Major results are presented with rigorous mathematical proofs, and references for further exploration are provided. Open problems in these areas are discussed, offering insights into recent developments and avenues for future research. Prerequisite topics such as differential geometry, measure theory, and group theory are incorporated in the main flow of the chapters, ensuring a comprehensive understanding. Junior researchers seeking an introduction to the field of sub-Riemannian geometry will find this an invaluable introductory companion. The book is also suitable for those entering research subjects on the interplay between geometry, analysis, and group theory. 2025-10-21T05:22:52Z 2025-10-21T05:22:52Z 2025-10-20T11:15:23Z 2025 book ONIX_20251020T130859_9783031988325_51 https://library.oapen.org/handle/20.500.12657/107685 9783031988325 9783031988318 https://directory.doabooks.org/handle/20.500.12854/168406 eng Graduate Texts in Mathematics; Mathematics and Statistics; Mathematics and Statistics (R0) open access image/jpeg n/a https://library.oapen.org/bitstream/20.500.12657/107685/1/9783031988325.pdf Springer Nature Springer 10.1007/978-3-031-98832-5 10.1007/978-3-031-98832-5 9fa3421d-f917-4153-b9ab-fc337c396b5a 24317701-2bc9-49ad-af05-8ce23f30a287 a88f7f15-e6f4-4051-8cdf-5a18b056d678 9783031988325 9783031988318 European Research Council (ERC) Springer 480 Cham [...] European Research Council ERC 10.13039/501100000781 open access |
| spellingShingle | Open Access Carnot-Carathéodory Space Nilpotent Lie Group Sub-Riemannian Geometry Sub-Finsler Geometry Heisenberg Group Heintze Group Pansu Theorem thema EDItEUR::P Mathematics and Science::PB Mathematics::PBM Geometry::PBMP Differential and Riemannian geometry Le Donne, Enrico Metric Lie Groups |
| title | Metric Lie Groups |
| title_full | Metric Lie Groups |
| title_fullStr | Metric Lie Groups |
| title_full_unstemmed | Metric Lie Groups |
| title_short | Metric Lie Groups |
| title_sort | metric lie groups |
| topic | Open Access Carnot-Carathéodory Space Nilpotent Lie Group Sub-Riemannian Geometry Sub-Finsler Geometry Heisenberg Group Heintze Group Pansu Theorem thema EDItEUR::P Mathematics and Science::PB Mathematics::PBM Geometry::PBMP Differential and Riemannian geometry |
| topic_facet | Open Access Carnot-Carathéodory Space Nilpotent Lie Group Sub-Riemannian Geometry Sub-Finsler Geometry Heisenberg Group Heintze Group Pansu Theorem thema EDItEUR::P Mathematics and Science::PB Mathematics::PBM Geometry::PBMP Differential and Riemannian geometry |
| url | ONIX_20251020T130859_9783031988325_51 |
| work_keys_str_mv | AT ledonneenrico metricliegroups |