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Smoothing properties and uniqueness of the weak Kaehler-Ricci flow

Geometric Flows in Riemannian and Complex Geometry May 02, 2016 - May 06, 2016

May 06, 2016 (02:00 PM PDT - 03:00 PM PDT)
Speaker(s): Eleonora Di Nezza (Institut de Mathématiques de Jussieu)
Location: MSRI:
  • complex geometry

  • Riemannian geometry

  • geometric analysis

  • geometric flow

  • Ricci flow

  • Kahler-Ricci flow

  • geometric measure theory

  • currents

Primary Mathematics Subject Classification
Secondary Mathematics Subject Classification No Secondary AMS MSC



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)

25964?type=thumb Di Nezza.Notes 570 KB application/pdf Download
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