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 language | English |
|---|---|
| Pages (from-to) | 153-162 |
| Number of pages | 10 |
| Journal | Journal of the Mathematical Society of Japan |
| Volume | 63 |
| Issue number | 1 |
| DOIs | |
| Publication status | Published - Sep 9 2011 |
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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 journal › Article
}
TY - JOUR
T1 - Height functions on surfaces with three critical values
AU - Morishita, Fumiya
AU - Saeki, Osamu
PY - 2011/9/9
Y1 - 2011/9/9
N2 - 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.
AB - 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.
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UR - http://www.scopus.com/inward/citedby.url?scp=80052392211&partnerID=8YFLogxK
U2 - 10.2969/jmsj/06310153
DO - 10.2969/jmsj/06310153
M3 - Article
VL - 63
SP - 153
EP - 162
JO - Journal of the Mathematical Society of Japan
JF - Journal of the Mathematical Society of Japan
SN - 0025-5645
IS - 1
ER -