Height functions on surfaces with three critical values

Fumiya Morishita, Osamu Saeki

Research output: Contribution to journalArticlepeer-review


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
Issue number1
Publication statusPublished - 2011

All Science Journal Classification (ASJC) codes

  • Mathematics(all)


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