On the Level Set of a Function with Degenerate Minimum Point
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....
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| Format: | Article |
| Language: | English |
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Hindawi Limited
2015-01-01
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| Series: | International Journal of Mathematics and Mathematical Sciences |
| Online Access: | http://dx.doi.org/10.1155/2015/493217 |