TL;DR
This paper studies long-term solutions of K"ahler-Ricci flows, focusing on controlling the flow's potential and exploring conditions like semi-ampleness for certain classes, to understand infinite time singularities.
Contribution
It provides new insights into the behavior of K"ahler-Ricci flows over infinite time, especially regarding potential control and semi-ampleness conditions.
Findings
Zero-order control on flow potential established
Conditions for infinite time singularities analyzed
Semi-ampleness linked to flow behavior
Abstract
We consider the general K\"ahler-Ricci flows which exist for all time. The zeroth order control on the flow metric potential for various infinite time singularities is the focus. The possible semi-amplness for numerically effective classes serves as the main motivation.
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Taxonomy
TopicsGeometry and complex manifolds · Geometric Analysis and Curvature Flows · Black Holes and Theoretical Physics