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

We prove a removal of singularities result for Bach-flat metrics in dimension4 under the assumption of bounded L^2 norm of curvature, bounded Sobolevconstant and a volume growth bound. This result extends the removal ofsingularities result for special classes of Bach-flat metrics obtained in\cite{TVMOD}. For the proof we analyze the decay rates of solutions to theBach-flat equation linearized around a flat metric. This classification is usedto prove that Bach-flat cones are in fact ALE of order $\tau$ for any $\tau <2$. This result is then used to prove the removal of singularities theorem.

Asymptotic curvature decay and removal of singularities of Bach-flat metrics