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Complex Geometry: Rigidity of $\kappa$-noncollapsed steady K\”ahler-Ricci Solitons April 04, 2016 (11:00 AM PDT - 12:00 PM PDT)
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Location: MSRI: Simons Auditorium
Speaker(s) Xiaohua Zhu (Peking University)
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As one of singular model solutions of Ricci flow, it is important to classify  $\kappa$-noncollapsed  steady Ricci solitons under a suitable curvature condition.    Perelman conjectured that all 3-dimensional $\kappa$-noncollapsed steady (gradient) Ricci solitons must be rotationally symmetric.  The conjecture is solved by Brendle in 2012.  For higher dimensions,  one may  guess that Perelman conjecture is true under positive curvature operator  condition.  In this talk, we focus on   $\kappa$-noncollapsed  steady  K\”ahler-Ricci Solitons  and show that such solitons should be flat under nonnegative bisectional curvature.  This is a joint work with Deng.

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