Regularity of Kähler–Ricci flows on Fano manifolds

Gang Tian; Zhenlei Zhang

doi:10.1007/s11511-016-0137-1

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Home > Journals > Acta Math. > Volume 216 > Issue 1 > Article

2016 Regularity of Kähler–Ricci flows on Fano manifolds

Gang Tian, Zhenlei Zhang

Author Affiliations +

Gang Tian,¹ Zhenlei Zhang²
¹School of Mathematical Sciences and Beijing International Center for Mathematical Research, Peking University; Department of Mathematics, Princeton University
²School of Mathematics, Capital Normal University

Acta Math. 216(1): 127-176 (2016). DOI: 10.1007/s11511-016-0137-1

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Abstract

In this paper, we will establish a regularity theory for the Kähler–Ricci flow on Fano n-manifolds with Ricci curvature bounded in L^p-norm for some ${p > n}$ . Using this regularity theory, we will also solve a long-standing conjecture for dimension 3. As an application, we give a new proof of the Yau–Tian–Donaldson conjecture for Fano 3-manifolds. The results have been announced in [45].

Funding Statement

The first author was supported by NSF grants. The second author was supported by a grant of Beijing MCE 11224010007 and NSFC 13210010022.

Citation

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Gang Tian. Zhenlei Zhang. "Regularity of Kähler–Ricci flows on Fano manifolds." Acta Math. 216 (1) 127 - 176, 2016. https://doi.org/10.1007/s11511-016-0137-1