Existence of Einstein metrics on Fano manifolds

Gang Tian

Research output: Chapter in Book/Report/Conference proceedingChapter

51 Scopus citations


It is a long-standing problem to establish the existence of Kähler-Einstein metrics on Fano manifolds since Yau’s solution for the Calabi conjecture in late 70s. It is also one of driving forces in today’s study in Kähler geometry. In this paper, we discuss a program I started more than twenty years ago on this famous problem. It includes some of my results and speculations on the existence of Kähler-Einstein metrics on Fano manifolds, such as, holomorphic invariants, the K-stability, the compactness theorem for Kähler-Einstein manifolds, the partial C0-estimates and their variations. I will also discuss some related problems as well as some recent advances.

Original languageEnglish (US)
Title of host publicationProgress in Mathematics
PublisherSpringer Basel
Number of pages41
StatePublished - 2012

Publication series

NameProgress in Mathematics
ISSN (Print)0743-1643
ISSN (Electronic)2296-505X

All Science Journal Classification (ASJC) codes

  • Analysis
  • Algebra and Number Theory
  • Geometry and Topology


  • Compactness theorems
  • Fano manifolds
  • Holomorphic invariants
  • K-stability
  • Kähler-Einstein metrics


Dive into the research topics of 'Existence of Einstein metrics on Fano manifolds'. Together they form a unique fingerprint.

Cite this