Height functions on surfaces with three critical values

Fumiya Morishita, Osamu Saeki

Research output: Contribution to journalArticle

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.

Original languageEnglish
Pages (from-to)153-162
Number of pages10
JournalJournal of the Mathematical Society of Japan
Volume63
Issue number1
DOIs
Publication statusPublished - Sep 9 2011

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Critical value
Critical point
Immersion
Distance Function
Closed

All Science Journal Classification (ASJC) codes

  • Mathematics(all)

Cite this

Height functions on surfaces with three critical values. / Morishita, Fumiya; Saeki, Osamu.

In: Journal of the Mathematical Society of Japan, Vol. 63, No. 1, 09.09.2011, p. 153-162.

Research output: Contribution to journalArticle

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