Mathematica Bohemica, Vol. 145, No. 1, pp. 71-73, 2020


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

Stephen J. Gardiner, Tomas Sjödin

Received August 24, 2018.   Published online March 5, 2019.

Abstract:  This note verifies a conjecture of Král, that a continuously differentiable function, which is subharmonic outside its critical set, is subharmonic everywhere.
Keywords:  subharmonic function; extension theorem
Classification MSC:  31B05


References:
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Affiliations:   Stephen J. Gardiner, School of Mathematics and Statistics, University College Dublin, Science Centre-North Belfield, Dublin 4, Ireland, e-mail: stephen.gardiner@ucd.ie; Tomas Sjödin, Department of Mathematics, Campus Valla, House B, Room 3A:681, Linköping University, 581 83, Linköping, Sweden, e-mail: tomas.sjodin@liu.se


 
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