Complete pluripolar curves and graphs

Volume 84 / 2004

Tomas Edlund Annales Polonici Mathematici 84 (2004), 75-86 MSC: Primary 32U05. DOI: 10.4064/ap84-1-8


It is shown that there exist $C^{\infty }$ functions on the boundary of the unit disk whose graphs are complete pluripolar. Moreover, for any natural number $k$, such functions are dense in the space of $C^k$ functions on the boundary of the unit disk. We show that this result implies that the complete pluripolar closed $C^\infty $ curves are dense in the space of closed $C^k$ curves in ${\mathbb C}^n$. We also show that on each closed subset of the complex plane there is a continuous function whose graph is complete pluripolar.


  • Tomas EdlundDepartment of Mathematics
    Uppsala University
    Box 480
    SE-751 06 Uppsala, Sweden

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