Riemann’s removable singularity theorem in several variables


Suppose V is a proper analytic variety in an open set UCn (that is of dimensionMathworldPlanetmath at most n-1) suppose that f:U\VC is holomorphic and further that f is locally bounded in U Then there exists a unique holomorphic extention of f to all of U.

If V is of even lower dimension we can in fact even drop the locally bounded requirement, see the Hartogs extension theorem.


  • 1 Steven G. Krantz. , AMS Chelsea Publishing, Providence, Rhode Island, 1992.
  • 2 Hassler Whitney. . Addison-Wesley, Philippines, 1972.
Title Riemann’s removable singularityMathworldPlanetmath theorem in several variables
Canonical name RiemannsRemovableSingularityTheoremInSeveralVariables
Date of creation 2013-03-22 15:34:57
Last modified on 2013-03-22 15:34:57
Owner jirka (4157)
Last modified by jirka (4157)
Numerical id 4
Author jirka (4157)
Entry type Theorem
Classification msc 30D30
Classification msc 32H02
Synonym Riemann’s extension theorem