Continuity of delta invariants and twisted Kahler-Einstein metrics

We show that delta invariant is a continuous function on the big cone. We will also introduce an analytic delta invariant in terms of the optimal exponent in the Moser- Trudinger inequality and prove that it varies continuously in the Kahler cone, from which we will deduce the continuity of the greatest Ricci lower bound. Then building on the work Berman-Boucksom-Jonsson, we obtain a uniform Yau- Tian-Donaldson theorem for twisted Kahler-Einstein metrics in transcendental cohomology classes. (c) 2021 Elsevier Inc. All rights reserved.

Automated summary

The article proves that the delta invariant is a continuous function on the big cone, introduces an analytic delta invariant related to the optimal exponent in the Moser-Trudinger inequality, and proves its continuous variation in the Kahler cone, deducing the continuity of the greatest Ricci lower bound. Building on the work of Berman-Boucksom-Jonsson, a uniform Yau-Tian-Donaldson theorem for twisted Kahler-Einstein metrics in transcendental cohomology classes is obtained.