Abstract
The J-flow is a parabolic flow on Kähler manifolds. It was defined by Donaldson in the setting of moment maps and by Chen as the gradient flow of the J-functional appearing in his formula for the Mabuchi energy. It is shown here that under a certain condition on the initial data, the J-flow converges to a critical metric. This is a generalization to higher dimensions of the author's previous work on Kähler surfaces. A corollary of this is the lower boundedness of the Mabuchi energy on Kähler classes satisfying a certain inequality when the first Chern class of the manifold is negative.
Citation
Ben Weinkove. "On the J-Flow in Higher Dimensions and the Lower Boundedness of the Mabuchi Energy." J. Differential Geom. 73 (2) 351 - 358, June 2006. https://doi.org/10.4310/jdg/1146169914
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