On the Level Set of a Function with Degenerate Minimum Point
Author
Source
International Journal of Mathematics and Mathematical Sciences
Issue
Vol. 2015, Issue 2015 (31 Dec. 2015), pp.1-6, 6 p.
Publisher
Hindawi Publishing Corporation
Publication Date
2015-07-08
Country of Publication
Egypt
No. of Pages
6
Main Subjects
Abstract EN
For n≥2, let M be an n-dimensional smooth closed manifold and f:M→R a smooth function.
We set minf(M)=m and assume that m is attained by unique point p∈M such that p is a nondegenerate critical point.
Then the Morse lemma tells us that if a is slightly bigger than m, f-1(a) is diffeomorphic to Sn-1.
In this paper, we relax the condition on p from being nondegenerate to being an isolated critical point and obtain the same consequence.
Some application to the topology of polygon spaces is also included.
American Psychological Association (APA)
Kamiyama, Yasuhiko. 2015. On the Level Set of a Function with Degenerate Minimum Point. International Journal of Mathematics and Mathematical Sciences،Vol. 2015, no. 2015, pp.1-6.
https://search.emarefa.net/detail/BIM-1066206
Modern Language Association (MLA)
Kamiyama, Yasuhiko. On the Level Set of a Function with Degenerate Minimum Point. International Journal of Mathematics and Mathematical Sciences No. 2015 (2015), pp.1-6.
https://search.emarefa.net/detail/BIM-1066206
American Medical Association (AMA)
Kamiyama, Yasuhiko. On the Level Set of a Function with Degenerate Minimum Point. International Journal of Mathematics and Mathematical Sciences. 2015. Vol. 2015, no. 2015, pp.1-6.
https://search.emarefa.net/detail/BIM-1066206
Data Type
Journal Articles
Language
English
Notes
Includes bibliographical references
Record ID
BIM-1066206