On stability and the convergence of the Kähler-Ricci flow

Details On stability and the convergence of the Kähler-Ricci flow On stability and the convergence of the Kähler-Ricci flow

2004-12-08

arxiv.org/abs/math/0412185v1

Mathematics

Differential Geometry

18 pages, no figure

Scientific paper

Assuming uniform bounds for the curvature, the exponential convergence of the
K\"ahler-Ricci flow is established under two conditions which are a form of
stability: the Mabuchi energy is bounded from below, and the dimension of the
space of holomorphic vector fields in an orbit of the diffeomorphism group
cannot jump up in the limit.

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