On a conjecture of Král concerning the subharmonic extension of continuously differentiable functions

Stephen J. Gardiner; Tomas Sjödin

Mathematica Bohemica (2020)

  • Volume: 145, Issue: 1, page 71-73
  • ISSN: 0862-7959

Abstract

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This note verifies a conjecture of Král, that a continuously differentiable function, which is subharmonic outside its critical set, is subharmonic everywhere.

How to cite

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Gardiner, Stephen J., and Sjödin, Tomas. "On a conjecture of Král concerning the subharmonic extension of continuously differentiable functions." Mathematica Bohemica 145.1 (2020): 71-73. <http://eudml.org/doc/297204>.

@article{Gardiner2020,
abstract = {This note verifies a conjecture of Král, that a continuously differentiable function, which is subharmonic outside its critical set, is subharmonic everywhere.},
author = {Gardiner, Stephen J., Sjödin, Tomas},
journal = {Mathematica Bohemica},
keywords = {subharmonic function; extension theorem},
language = {eng},
number = {1},
pages = {71-73},
publisher = {Institute of Mathematics, Academy of Sciences of the Czech Republic},
title = {On a conjecture of Král concerning the subharmonic extension of continuously differentiable functions},
url = {http://eudml.org/doc/297204},
volume = {145},
year = {2020},
}

TY - JOUR
AU - Gardiner, Stephen J.
AU - Sjödin, Tomas
TI - On a conjecture of Král concerning the subharmonic extension of continuously differentiable functions
JO - Mathematica Bohemica
PY - 2020
PB - Institute of Mathematics, Academy of Sciences of the Czech Republic
VL - 145
IS - 1
SP - 71
EP - 73
AB - This note verifies a conjecture of Král, that a continuously differentiable function, which is subharmonic outside its critical set, is subharmonic everywhere.
LA - eng
KW - subharmonic function; extension theorem
UR - http://eudml.org/doc/297204
ER -

References

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  1. Armitage, D. H., Gardiner, S. J., 10.1007/978-1-4471-0233-5, Springer Monographs in Mathematics. Springer, London (2001). (2001) Zbl0972.31001MR1801253DOI10.1007/978-1-4471-0233-5
  2. Caffarelli, L. A., Cabré, X., 10.1090/coll/043, Colloquium Publications 43. AMS, Providence (1995). (1995) Zbl0834.35002MR1351007DOI10.1090/coll/043
  3. Crandall, M. G., Ishii, H., Lions, P.-L., 10.1090/S0273-0979-1992-00266-5, Bull. Am. Math. Soc., New Ser. 27 (1992), 1-67. (1992) Zbl0755.35015MR1118699DOI10.1090/S0273-0979-1992-00266-5
  4. Juutinen, P., Lindqvist, P., 10.4310/MRL.2004.v11.n1.a4, Math. Res. Lett. 11 (2004), 31-34. (2004) Zbl1153.35324MR2046197DOI10.4310/MRL.2004.v11.n1.a4
  5. Juutinen, P., Lindqvist, P., Manfredi, J. J., 10.1137/S0036141000372179, SIAM J. Math. Anal. 33 (2001), 699-717. (2001) Zbl0997.35022MR1871417DOI10.1137/S0036141000372179
  6. Král, J., 10.1112/jlms/s2-28.1.62, J. Lond. Math. Soc., II. Ser. 28 (1983), 62-70. (1983) Zbl0526.31003MR0703465DOI10.1112/jlms/s2-28.1.62
  7. Král, J., 10.21136/CPM.1985.118241, Čas. Pěst. Mat. 110 (1985), page 415 Czech. (1985) DOI10.21136/CPM.1985.118241
  8. Pokrovskiĭ, A. V., 10.15407/dopovidi2015.07.029, Dopov. Nats. Akad. Nauk Ukr., Mat. Pryr. Tekh. Nauky 2015 (2015), 29-31. (2015) Zbl1340.30135MR3718287DOI10.15407/dopovidi2015.07.029
  9. Rudin, W., Real and Complex Analysis, McGraw-Hill Book Co., New York (1987). (1987) Zbl0925.00005MR0924157

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