Natural pseudodistances between closed manifolds

@article{Donatini2004NaturalPB,
  title={Natural pseudodistances between closed manifolds},
  author={Pietro Donatini and Patrizio Frosini},
  journal={Forum Mathematicum},
  year={2004},
  volume={16}
}
Let us consider two closed homeomorphic manifolds M;N of class C 1 and two functions j : M ! R, c : N ! R of class C . The natural pseudodistance d between the pairs ðM; jÞ; ðN;cÞ is defined as the infimum of Yð f Þ 1⁄4 def maxP AMjjðPÞ cð f ðPÞÞj, as f varies in the set of all homeomorphisms from M onto N. In this paper we prove that a suitable multiple of d by a positive integer k coincides with the distance between two critical values of the functions j;c. 2000 Mathematics Subject… 

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