English (United Kingdom)

https://curated-unify.zendy.io/wp-json/zendy-region/v1/featured_content/oa?rat=en

https://curated-unify.zendy.io/wp-json/zendy-region/v1/highlighted_journal/

Global: Zendy Plus annual

Presents the access of premium content as premium feature

Premium Content

Presents the keyphrase highlighting as premium feature

Keyphrase Highlighting

Presents the summarisation as premium feature

Summarisation

Insights

Presents the pdf analysis as premium feature

PDF Analysis

Presents the zaia usage as premium feature

ZAIA

Global: Zendy Tools annual

Global: Zendy Free Plan

Global: Zendy Tools monthly

Global: Zendy Plus monthly

Theorem I has been an outstanding conjecture. This author first heard the conjecture mentioned by Lelong in the 1972 Several Complex Variables Conference in Poitiers, France, and later learned that it was also mentioned in [6] and by Harvey in the 1971 Berkeley Summer Conference on Partial Differential Equations. Some partial results in this direction have been obtained. Thie [12] proved that, when u is defined by integration over an analytic subset of pure codimension fc, the Lelong number agrees with the multiplicity of the analytic set and hence the conjecture is true in this case. King [7] proved that, if the Lelong number of u is an integer at almost every point of its support with respect to the Hausdorff (2n — 2k)measure, then M is a linear combination of currents defined by integration over analytic subsets of pure codimension fc, and, as a consequence, the conjecture is true in this case. Harvey and King [6] improved the result of [7] and showed that if, for every compact subset K of Supp w, there exists c > 0 such that the Lelong number of u at x is ^ c for almost all x e K with respect to the Hausdorff (2n — 2fc)-measure, then u is a linear combination of currents defined by integration over analytic subsets of pure codimension fc, and, consequently, the conjecture is true in this case. Recently Skoda [11] proved that, if the domain D where u is defined is Stein, then for every c ^ 0 there exists an analytic subset Xc of D such that

Analyticity of sets associated to Lelong numbers and the extension of meromorphic maps