Exceptional Sets for Subharmonic Functions


 Subharmonic, Hausdorff measure, exceptional sets.

How to Cite

Juhani Riihentaus. (2015). Exceptional Sets for Subharmonic Functions. Journal of Basic & Applied Sciences, 11, 567–571. https://doi.org/10.6000/1927-5129.2015.11.75


Blanchet has shown that hypersurfaces of class C1 are removable singularities for subharmonic functions, provided the considered subharmonic functions satisfy certain assumptions. Later we showed that, in certain cases, it is sufficient that the exceptional sets are of finite (n-1)-dimensional Hausdorff measure. Now we improve our results still further, relaxing our previous assumptions imposed on the considered subharmonic functions.



Blanchet P. On removable singularities of subharmonic and plurisubharmonic functions. Complex Variables 1995; 26: 311-22. http://dx.doi.org/10.1080/17476939508814792

Riihentaus J. Subharmonic functions, mean value inequality, boundary behavior, nonintegrability and exceptional sets. Workshop on Potential Theory and Free Boundary Flows; August 19-27, 2003: Kiev, Ukraine. In: Transactions of the Institute of Mathematics of the National Academy of Sciences of Ukraine 2004; Kiev; 1(no. 3): 169-91.

Riihentaus J. An inequality type condition for quasinearly subharmonic functions and applications. Positivity VII, Leiden, July 22-26, 2013, Zaanen Centennial Conference. In: Trends in Mathematical Series, Birkhäuser, to appear.

Helms LL. Introduction to potential theory. New York: Wiley-Interscience 1969.

Hervé M. Analytic and plurisubharmonic functions in finite and infinite dimensional spaces. Lecture Notes in Mathematics 198. Berlin: Springer 1971.

Lelong P. Plurisubharmonic functions and positive differential forms. New York: Gordon and Breach 1969.

Rado T. Subharmonic functions. Berlin: Springer 1937.

Federer H. Geometric measure theory. Berlin: Springer 1969.

Rudin W. Real and Complex Analysis. New Delhi: Tata McGraw-Hill 1979.

Creative Commons License

This work is licensed under a Creative Commons Attribution-NonCommercial 4.0 International License.

Copyright (c) 2015 Juhani Riihentaus