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    STUDIA MATHEMATICA - Issue no. 4 / 2013  
         
  Article:   THE MINIMUM NUMBER OF CRITICAL POINTS OF CIRCULAR MORSE FUNCTIONS.

Authors:  DORIN ANDRICA, CORNEL PINTEA.
 
       
         
  Abstract:   The minimum number of critical points for circular Morse functions on closed connected surfaces has been computed by the authors in [4]. Some bounds for the minimum characteristic number of closed connected orientable surfaces embedded in the first Heisenberg group with respect to its horizontal distribution are also given by [4]. In this paper we provide a more elementary proof for the minimum number of critical points of circular Morse functions and the details for the bounds on the mentioned minimum characteristic number.

Mathematics Subject Classification (2010): 58E05.
Keywords: Circular Morse function.
 
         
     
         
         
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