Riemannian manifolds are KKM spaces
Let (M, g) be a complete, finite-dimensional Riemannian manifold. Based on the fact that any geodesic convex subset of M is a KKM space, we establish the KKM theory on such subsets originated from the Knaster-Kuratowski-Mazurkiewicz theorem in 1929.
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| Format: | Article |
| Language: | English |
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ATNAA
2019-05-01
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| Series: | Advances in the Theory of Nonlinear Analysis and its Applications |
| Subjects: | |
| Online Access: | https://dergipark.org.tr/en/download/article-file/707268 |
| _version_ | 1797905732575690752 |
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| author | Sehie Park |
| author_facet | Sehie Park |
| author_sort | Sehie Park |
| collection | DOAJ |
| description | Let (M, g) be a complete, finite-dimensional Riemannian manifold. Based on the fact that any geodesic
convex subset of M is a KKM space, we establish the KKM theory on such subsets originated from the
Knaster-Kuratowski-Mazurkiewicz theorem in 1929. |
| first_indexed | 2024-04-10T10:09:54Z |
| format | Article |
| id | doaj.art-33102db850c546a0806720d69caf8ba3 |
| institution | Directory Open Access Journal |
| issn | 2587-2648 2587-2648 |
| language | English |
| last_indexed | 2024-04-10T10:09:54Z |
| publishDate | 2019-05-01 |
| publisher | ATNAA |
| record_format | Article |
| series | Advances in the Theory of Nonlinear Analysis and its Applications |
| spelling | doaj.art-33102db850c546a0806720d69caf8ba32023-02-15T16:22:13ZengATNAAAdvances in the Theory of Nonlinear Analysis and its Applications2587-26482587-26482019-05-0132647310.31197/atnaa.513857Riemannian manifolds are KKM spacesSehie Park0The National Academy of Sciences, Republic of Korea, Seoul 06579, KOREA; Department of Mathematical Sciences, Seoul National University, Seoul 08826, KOREALet (M, g) be a complete, finite-dimensional Riemannian manifold. Based on the fact that any geodesic convex subset of M is a KKM space, we establish the KKM theory on such subsets originated from the Knaster-Kuratowski-Mazurkiewicz theorem in 1929.https://dergipark.org.tr/en/download/article-file/707268riemannian manifoldkkm theoremabstract convex spacegeodesic convex set. |
| spellingShingle | Sehie Park Riemannian manifolds are KKM spaces Advances in the Theory of Nonlinear Analysis and its Applications riemannian manifold kkm theorem abstract convex space geodesic convex set. |
| title | Riemannian manifolds are KKM spaces |
| title_full | Riemannian manifolds are KKM spaces |
| title_fullStr | Riemannian manifolds are KKM spaces |
| title_full_unstemmed | Riemannian manifolds are KKM spaces |
| title_short | Riemannian manifolds are KKM spaces |
| title_sort | riemannian manifolds are kkm spaces |
| topic | riemannian manifold kkm theorem abstract convex space geodesic convex set. |
| url | https://dergipark.org.tr/en/download/article-file/707268 |
| work_keys_str_mv | AT sehiepark riemannianmanifoldsarekkmspaces |