The number of topologically non-equivalent minimal functions on closed surfaces
We consider two classes of smooth functions with three critical values on smooth closed surface of genus $g\geq1$, that possess only one (degenerate) saddle critical point in addition to $k$ local maxima and $l$ local minima. Namely: $C_{k,l}(M_g)$ is the class of such functions on oriented surface...
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| Datum: | 2015 |
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| Ключові слова: | keywords |
| Hauptverfasser: | , |
| Format: | Artikel |
| Sprache: | Ukrainisch |
| Veröffentlicht: |
Інститут математики НАН України
2015
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| Online Zugang: | https://trim.imath.kiev.ua/index.php/trim/article/view/135 |
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| Назва журналу: | Transactions of Institute of Mathematics of NAS of Ukraine |
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Transactions of Institute of Mathematics of NAS of Ukraine| Zusammenfassung: | We consider two classes of smooth functions with three critical values on smooth closed surface of genus $g\geq1$, that possess only one (degenerate) saddle critical point in addition to $k$ local maxima and $l$ local minima. Namely: $C_{k,l}(M_g)$ is the class of such functions on oriented surface $M_g$ and $C_{k,l}(N_g)$ -- on non-oriented surface $N_g$. In this paper we calculate the number of topologically non-equivalent (minimal) functions from the class $C_{1,1}(M_g)$ for all $g\geq 1$and from the class $C_{1,1}(N_g)$ for $g=5, 6$. Asymptotic estimate for number of topologically non-equivalent functions from the class $C_{1,1}(N_g)$ (as $g\to\infty$) are also established. |
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