Abstract
The paper contains a full geometric characterization of compact semialgebraic sets in C satisfying the Łojasiewicz-Siciak condition. The Łojasiewicz-Siciak condition is a certain estimate for the Siciak extremal function. In a previous paper, we gave a sufficient criterion for a compact, connected, and semialgebraic set in C to satisfy this condition. In the present paper, we remove completely the connectedness assumption and prove that the aforementioned sufficient condition is also necessary. Moreover, we obtain some new results concerning the Łojasiewicz-Siciak condition in C N . For example, we prove that if K 1,...,K p are compact, nonpluripolar, and pairwise disjoint subsets of C N , each satisfying the Łojasiewicz-Siciak condition, and K:= K 1⋃· · ·⋃K p is polynomially convex, then K satisfies this condition as well.
Sign-in/Register to access full text options 
Talk to us
Join us for a 30 min session where you can share your feedback and ask us any queries you have
Schedule a callDisclaimer: All third-party content on this website/platform is and will remain the property of their respective owners and is provided on "as is" basis without any warranties, express or implied. Use of third-party content does not indicate any affiliation, sponsorship with or endorsement by them. Any references to third-party content is to identify the corresponding services and shall be considered fair use under The CopyrightLaw.
