K-stability implies CM-stability

Gang Tian

Research output: Contribution to journalArticlepeer-review

7 Scopus citations


In this paper, we prove in details that any polarized K-stable manifold is CM-stable. This extends what I did for Fano manifolds in my 2012 paper. Our proof is based on an asymptotic formula for the K-energy and S. Paul’s works ([Pa08], [Pa12], [Pa13]) on the K-stability in terms of stable pairs.

Original languageEnglish (US)
Pages (from-to)245-261
Number of pages17
JournalProgress in Mathematics
StatePublished - 2017

All Science Journal Classification (ASJC) codes

  • Analysis
  • Algebra and Number Theory
  • Geometry and Topology


  • CM-weight
  • Determinant line bundle
  • K-stability
  • Polarization


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