Hartogs extension theorem


Suppose V is an analytic variety in an open set UCn (n2) of dimensionMathworldPlanetmath at most n-2 and suppose that f:U\VC is holomorphic. Then there exists a unique holomorphic extention of f to all of U.

Note that when V is 0 dimensional (a point) then this is just a special case of the Hartogs’ phenomenon. Also note the similarity to Riemann’s removable singularityMathworldPlanetmath theorem in several variables, where however we also assume that f is locally bounded.


  • 1 Steven G. Krantz. , AMS Chelsea Publishing, Providence, Rhode Island, 1992.
  • 2 Hassler Whitney. . Addison-Wesley, Philippines, 1972.
Title Hartogs extension theorem
Canonical name HartogsExtensionTheorem
Date of creation 2013-03-22 15:34:54
Last modified on 2013-03-22 15:34:54
Owner jirka (4157)
Last modified by jirka (4157)
Numerical id 4
Author jirka (4157)
Entry type Theorem
Classification msc 32H02