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

Let $(X, D)$ be a log variety with an effective holomorphic torus action, and$\Theta$ be a closed positive $(1,1)$-current. For any smooth positive function$g$ defined on the moment polytope of the torus action, we study theMonge-Amp\`{e}re equations that correspond to generalized and twistedK\"{a}hler-Ricci $g$-solitons. We prove a version of Yau-Tian-Donaldson (YTD)conjecture for these general equations, showing that the existence of solutionsis always equivalent to an equivariantly uniform $\Theta$-twisted$g$-Ding-stability. When $\Theta$ is a current associated to a torus invariantlinear system, we further show that equivariant special test configurationssuffice for testing the stability. Our results allow arbitrary kltsingularities and generalize most of previous results on (uniform) YTDconjecture for (twisted) K\"{a}hler-Ricci/Mabuchi solitons orK\"{a}hler-Einstein metrics.

On the Yau-Tian-Donaldson conjecture for generalized K\"ahler-Ricci soliton equations