A Note on Starshaped Sets in 2-Dimensional Manifolds without Conjugate Points
Let Wn be C∞ complete, simply connected n-dimensional Riemannian manifolds without conjugate points. Assume that S⊂W2 is starshaped where kerS≠S. For every point x∈S∖kerS, define A(x)={y: y lies on some geodesic segment in S from x to a point of kerS}. There is a finite collection A of all maximal A...
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| Format: | Article |
| Language: | English |
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Wiley
2014-01-01
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| Series: | Journal of Function Spaces |
| Online Access: | http://dx.doi.org/10.1155/2014/675735 |
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| author | Adem Kılıcman Wedad Saleh |
| author_facet | Adem Kılıcman Wedad Saleh |
| author_sort | Adem Kılıcman |
| collection | DOAJ |
| description | Let Wn be C∞ complete, simply connected n-dimensional Riemannian manifolds without conjugate points. Assume that S⊂W2 is starshaped where kerS≠S. For every point x∈S∖kerS, define A(x)={y: y lies on some geodesic segment in S from x to a point of kerS}. There is a finite collection A of all maximal A sets whose union is S. Further, kerS=∩{A:A in A}. |
| format | Article |
| id | doaj-art-7da76d92860c4befb877c03b68e219dd |
| institution | Kabale University |
| issn | 2314-8896 2314-8888 |
| language | English |
| publishDate | 2014-01-01 |
| publisher | Wiley |
| record_format | Article |
| series | Journal of Function Spaces |
| spelling | doaj-art-7da76d92860c4befb877c03b68e219dd2025-02-03T01:31:56ZengWileyJournal of Function Spaces2314-88962314-88882014-01-01201410.1155/2014/675735675735A Note on Starshaped Sets in 2-Dimensional Manifolds without Conjugate PointsAdem Kılıcman0Wedad Saleh1Department of Mathematics and Institute for Mathematical Research, Universiti Putra Malaysia (UPM), 43400 Serdang, Selangor, MalaysiaDepartment of Mathematics and Institute for Mathematical Research, Universiti Putra Malaysia (UPM), 43400 Serdang, Selangor, MalaysiaLet Wn be C∞ complete, simply connected n-dimensional Riemannian manifolds without conjugate points. Assume that S⊂W2 is starshaped where kerS≠S. For every point x∈S∖kerS, define A(x)={y: y lies on some geodesic segment in S from x to a point of kerS}. There is a finite collection A of all maximal A sets whose union is S. Further, kerS=∩{A:A in A}.http://dx.doi.org/10.1155/2014/675735 |
| spellingShingle | Adem Kılıcman Wedad Saleh A Note on Starshaped Sets in 2-Dimensional Manifolds without Conjugate Points Journal of Function Spaces |
| title | A Note on Starshaped Sets in 2-Dimensional Manifolds without Conjugate Points |
| title_full | A Note on Starshaped Sets in 2-Dimensional Manifolds without Conjugate Points |
| title_fullStr | A Note on Starshaped Sets in 2-Dimensional Manifolds without Conjugate Points |
| title_full_unstemmed | A Note on Starshaped Sets in 2-Dimensional Manifolds without Conjugate Points |
| title_short | A Note on Starshaped Sets in 2-Dimensional Manifolds without Conjugate Points |
| title_sort | note on starshaped sets in 2 dimensional manifolds without conjugate points |
| url | http://dx.doi.org/10.1155/2014/675735 |
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