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 Tools annual

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 monthly

Global: Zendy Plus monthly

Presents the access of premium content as premium feature

Premium Content

Global: Zendy Plus annual

Global: Zendy Free Plan

Consider a complex line bundle over a compact complex manifold equipped withan infinitely differentiable metric with strictly positive curvature form.Assign to positive tensor powers of this bundle the associated product metricsand Bergman projection operators. Zelditch has conjectured that if the Bergmankernels, away from the diagonal, decay exponentially fast to zero as the powertends to infinity, then the metric must be real analytic. Moreover, this isconjectured even if exponential decay is assumed to hold merely for somearbitrarily sparse subsequence of powers tending to infinity.  Previously the author has constructed examples in which the metric isinfinitely differentiable, but exponential decay does not hold. These examplesare within a framework in which a certain degree of symmetry is present. In thepresent paper we prove the conjecture for all structures within this framework,thus providing evidence in favor of the conjecture. The analysis is carried outfor base manifolds of arbitrary dimensions, rather than only for dimension oneas in the author's previous work.

Off-diagonal decay of Bergman kernels: On a conjecture of Zelditch