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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Hindawi Limited
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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doaj-7da76d92860c4befb877c03b68e219dd2020-11-24T20:56:50ZengHindawi LimitedJournal 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 |
| collection |
DOAJ |
| language |
English |
| format |
Article |
| sources |
DOAJ |
| author |
Adem Kılıcman Wedad Saleh |
| spellingShingle |
Adem Kılıcman Wedad Saleh A Note on Starshaped Sets in 2-Dimensional Manifolds without Conjugate Points Journal of Function Spaces |
| author_facet |
Adem Kılıcman Wedad Saleh |
| author_sort |
Adem Kılıcman |
| title |
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_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_sort |
note on starshaped sets in 2-dimensional manifolds without conjugate points |
| publisher |
Hindawi Limited |
| series |
Journal of Function Spaces |
| issn |
2314-8896 2314-8888 |
| publishDate |
2014-01-01 |
| 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}. |
| url |
http://dx.doi.org/10.1155/2014/675735 |
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AT ademkılıcman anoteonstarshapedsetsin2dimensionalmanifoldswithoutconjugatepoints AT wedadsaleh anoteonstarshapedsetsin2dimensionalmanifoldswithoutconjugatepoints AT ademkılıcman noteonstarshapedsetsin2dimensionalmanifoldswithoutconjugatepoints AT wedadsaleh noteonstarshapedsetsin2dimensionalmanifoldswithoutconjugatepoints |
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