• Corpus ID: 237091350

On Morse Index Retrieval

  title={On Morse Index Retrieval},
  author={Daniil Mamaev},
A smooth function f in a neighbourhood of the unit sphere Sn−1 is said to admit index λ if it can be extended to a function F in the unit ball B such that F has a unique critical point p and the Morse index of p is equal to λ. It is easy to see that a function f cannot admit two indices of different parity. We prove that for any two indices that differ by two there exists a function f that admits both of them. 

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