Existence of Einstein metrics on Fano manifolds

Gang Tian

Research output: Chapter in Book/Report/Conference proceedingChapter

36 Scopus citations

Abstract

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
Pages119-159
Number of pages41
DOIs
StatePublished - Jan 1 2012

Publication series

NameProgress in Mathematics
Volume297
ISSN (Print)0743-1643
ISSN (Electronic)2296-505X

All Science Journal Classification (ASJC) codes

  • Analysis
  • Algebra and Number Theory
  • Geometry and Topology

Keywords

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

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  • Cite this

    Tian, G. (2012). Existence of Einstein metrics on Fano manifolds. In Progress in Mathematics (pp. 119-159). (Progress in Mathematics; Vol. 297). Springer Basel. https://doi.org/10.1007/978-3-0348-0257-4_5