On level sets of a pseudoharmonic function on a plane

Authors

  • Ye.O. Polulyakh

DOI:

https://doi.org/10.15407/dopovidi2014.01.022

Keywords:

plane, pseudoharmonic function, sets

Abstract

Let T be a forest, which consists of a finite number of locally finite trees. Let V0 be the set of all vertices of T of degree 1. We propose a sufficient condition for the image of an embedding Ψ: T \ V0 → R2 to be a level set of a pseudoharmonic function.

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References

Poluyakh Ye. Ukr. mat. zhurn., 2013, 65, No. 7: 975–995 (in Ukrainian).

Morse M. Topological methods in the theory of functions of a complex variable. Princeton: Inst. for Adv. Study, 1947.

Polulyakh E., Yurchuk I. On the pseudo-harmonic functions defined on a disk. In: Proceedings of the Institute of Mathematics NAS of Ukraine. Vol. 80. Kyiv, 2009.

Sharko V. V. Dopov. Nac. akad. nauk Ukr., 2013, No. 4: 23–35 (in Russian).

Sharko V. V. Zb. prats Inst. matematyky NAN Ukr., 2013, 7, No. 1: 534–543 (in Russian).

Tôki Y. Osaka Math. J., 1951, 3, No. 1: 101–122.

Published

24.03.2025

How to Cite

Polulyakh, Y. (2025). On level sets of a pseudoharmonic function on a plane . Reports of the National Academy of Sciences of Ukraine, (1), 22–26. https://doi.org/10.15407/dopovidi2014.01.022