Smoothing properties and uniqueness of the weak Kaehler-Ricci flow
Geometric Flows in Riemannian and Complex Geometry May 02, 2016 - May 06, 2016
Location: SLMath:
complex geometry
Riemannian geometry
geometric analysis
geometric flow
Ricci flow
Kahler-Ricci flow
geometric measure theory
currents
51D25 - Lattices of subspaces and geometric closure systems [See also 05B35]
51D30 - Continuous geometries, geometric closure systems and related topics [See also 06Cxx]
51E05 - General block designs in finite geometry [See also 05B05]
14510
Let X be a compact Kaehler manifold. I will show that the Kaehler-Ricci flow can be run from a degenerate initial data, (more precisely, from an arbitrary positive closed current) and that it is immediately smooth in a Zariski open subset of X. Moreover, if the initial data has positive Lelong number we indeed have propagation of singularities for short time. Finally, I will prove a uniqueness result in the case of zero Lelong numbers.
(This is a joint work with Chinh Lu)
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