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 consider a subset  S  of the complex Lie algebra ( n , ℂ) and the cone  C ( S ) of curvature operators which are nonnegative on  S . We show that  C ( S ) defines a Ricci flow invariant curvature condition if  S  is invariant under Ad SO( n , ℂ) . The analogue for Kähler curvature operators holds as well. Although the proof is very simple and short, it recovers all previously known invariant nonnegativity conditions. As an application we reprove that a compact Kähler manifold with positive orthogonal bisectional curvature evolves to a manifold with positive bisectional curvature and is thus biholomorphic to ℂℙ  n  . Moreover, the methods can also be applied to prove Harnack inequalities.

A Lie algebraic approach to Ricci flow invariant curvature conditions and Harnack inequalities