A note on starshaped sets in 2-dimensional manifolds without conjugate points
Let W n be C ∞ complete, simply connected n-dimensional Riemannian manifolds without conjugate points. Assume that n=2 and S⊂W 2 is starshaped where ker S≠S. For every point x∈S∖ ker S, define A(x)={y:y lies on some geodesic segment inf S form x to a point of ker S}. There is a finite collection A o...
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Hindawi Publishing Corporation
2014
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Online Access: | http://psasir.upm.edu.my/id/eprint/36210/1/A%20note%20on%20starshaped%20sets%20in%202.pdf http://psasir.upm.edu.my/id/eprint/36210/ http://www.hindawi.com/journals/jfs/2014/675735/abs/ |
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my.upm.eprints.362102015-09-18T00:25:20Z http://psasir.upm.edu.my/id/eprint/36210/ A note on starshaped sets in 2-dimensional manifolds without conjugate points Kilicman, Adem Saleh, Wedad Let W n be C ∞ complete, simply connected n-dimensional Riemannian manifolds without conjugate points. Assume that n=2 and S⊂W 2 is starshaped where ker S≠S. For every point x∈S∖ ker S, define A(x)={y:y lies on some geodesic segment inf S form x to a point of ker S}. There is a finite collection A of all maximal A sets whose union is S. Further, ker S=∩{A:AinA}. Hindawi Publishing Corporation 2014 Article PeerReviewed application/pdf en http://psasir.upm.edu.my/id/eprint/36210/1/A%20note%20on%20starshaped%20sets%20in%202.pdf Kilicman, Adem and Saleh, Wedad (2014) A note on starshaped sets in 2-dimensional manifolds without conjugate points. Journal of Function Spaces, 2014. art. no. 675735. pp. 1-3. ISSN 2314-8896; ESSN: 2314-8888 http://www.hindawi.com/journals/jfs/2014/675735/abs/ 10.1155/2014/675735 |
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Let W n be C ∞ complete, simply connected n-dimensional Riemannian manifolds without conjugate points. Assume that n=2 and S⊂W 2 is starshaped where ker S≠S. For every point x∈S∖ ker S, define A(x)={y:y lies on some geodesic segment inf S form x to a point of ker S}. There is a finite collection A of all maximal A sets whose union is S. Further, ker S=∩{A:AinA}. |
format |
Article |
author |
Kilicman, Adem Saleh, Wedad |
spellingShingle |
Kilicman, Adem Saleh, Wedad A note on starshaped sets in 2-dimensional manifolds without conjugate points |
author_facet |
Kilicman, Adem Saleh, Wedad |
author_sort |
Kilicman, Adem |
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 Publishing Corporation |
publishDate |
2014 |
url |
http://psasir.upm.edu.my/id/eprint/36210/1/A%20note%20on%20starshaped%20sets%20in%202.pdf http://psasir.upm.edu.my/id/eprint/36210/ http://www.hindawi.com/journals/jfs/2014/675735/abs/ |
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13.18916 |