Complete pluripolar curves and graphs

• Autorzy: Tomas Edlund
• Języki publikacji: EN

Abstrakty

EN

It is shown that there exist $C^{∞}$ 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 $C^∞$ curves are dense in the space of closed $C^k$ curves in ℂⁿ. We also show that on each closed subset of the complex plane there is a continuous function whose graph is complete pluripolar.

• Wydawca: Institute of Mathematics Polish Academy of Sciences
• Czasopismo: Annales Polonici Mathematici
• Rocznik: 2004
• Tom: 84
• Numer: 1
• Strony: 75-86

Daty

wydano

2004

Twórcy

autor

Tomas Edlund

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

Identyfikatory

DOI

10.4064/ap84-1-8