Journal of the Mathematical Society of Japan
- J. Math. Soc. Japan
- Volume 63, Number 1 (2011), 153-162.
Height functions on surfaces with three critical values
For a given closed surface, we study height functions with three critical values associated with immersions of the surface into 3-space, where the critical points may not be non-degenerate. We completely characterize the numbers of critical points corresponding to the three critical values that can be realized by such height functions. We also study the cases where the immersion can be replaced by an embedding or the critical points are all non-degenerate. Similar problems are studied for distance functions as well.
J. Math. Soc. Japan, Volume 63, Number 1 (2011), 153-162.
First available in Project Euclid: 27 January 2011
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MORISHITA, Fumiya; SAEKI, Osamu. Height functions on surfaces with three critical values. J. Math. Soc. Japan 63 (2011), no. 1, 153--162. doi:10.2969/jmsj/06310153. https://projecteuclid.org/euclid.jmsj/1296138347