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 Plus monthly

Global: Zendy Tools annual

Global: Zendy Tools monthly

Global: Zendy Free Plan

We show that a simply-connected closed four-dimensional Ricci flow whoseRicci curvature is uniformly bounded below and whose volume does not approachzero must converge to a $C^{0}$ orbifold at any finite-time singularity, so hasan extension through the singularity via orbifold Ricci flow. Moreover, aType-I blowup of the flow based at any orbifold point converges to a flat conein the Gromov-Hausdorff sense, without passing to a subsequence. In addition,we prove $L^{p}$ bounds for the curvature tensor on time-slices for any $p<2$.In higher dimensions, we show that every singular point of the flow is aType-II point, and that any tangent flow at a singular point is a static flowcorresponding to a Ricci flat cone.

Ricci Flow with Ricci Curvature and Volume Bounded Below