Dimension of pluripolar sets - MathOverflow most recent 30 from http://mathoverflow.net 2013-05-18T20:06:50Z http://mathoverflow.net/feeds/question/50914 http://www.creativecommons.org/licenses/by-nc/2.5/rdf http://mathoverflow.net/questions/50914/dimension-of-pluripolar-sets Dimension of pluripolar sets stefano Trapani 2011-01-02T08:31:36Z 2011-01-02T12:48:25Z <p>Let $\Omega$ be an open set in $\mathbb C^n$, and let $A$ be a closed pluripolar set in $\Omega$. Is there a notion of dimension of $A$ such that the following theorem is true?</p> <p><strong>Theorem.</strong> </p> <p>Let $\phi$ be a plurisubharmonic function on $\Omega \setminus A$ (not necessarly assumed to be locally bounded above near $A$), and assume that the (real) codimension of $A$ is at least $3$. Then the function $\phi$ extends to a plurisubharmonic function on $\Omega$. </p> <p>I think I can prove the theorem in case $A$ is complex analytic.</p>