Journal of the Mathematical Society of Japan

Height functions on surfaces with three critical values

Fumiya MORISHITA and Osamu SAEKI

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Abstract

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.

Article information

Source
J. Math. Soc. Japan, Volume 63, Number 1 (2011), 153-162.

Dates
First available in Project Euclid: 27 January 2011

Permanent link to this document
https://projecteuclid.org/euclid.jmsj/1296138347

Digital Object Identifier
doi:10.2969/jmsj/06310153

Mathematical Reviews number (MathSciNet)
MR2752435

Zentralblatt MATH identifier
1229.58031

Subjects
Primary: 58K05: Critical points of functions and mappings
Secondary: 57R45: Singularities of differentiable mappings 57R42: Immersions

Keywords
height function critical point critical value immersion embedding

Citation

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


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References

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