Scalar curvature, conformal geometry, and the Ricci flow with surgery

Research output: Chapter in Book/Report/Conference proceedingConference contribution

1 Scopus citations

Abstract

In this note we will review recent results concerning two geometric problems associated to the scalar curvature. In the first part we will review the solution to Schoen's conjecture about the compactness of the set of solutions to the Yamabe problem. It has been discovered, in a series of three papers, that the conjecture is true if and only if the dimension is less than or equal to 24. In the second part we will discuss the connectedness of the moduli space of metrics with positive scalar curvature in dimension three. In two dimensions this was proved by Weyl in 1916. This is a geometric application of the Ricci flow with surgery and Perelman's work on Hamilton's Ricci flow.

Original languageEnglish (US)
Title of host publicationProceedings of the International Congress of Mathematicians 2010, ICM 2010
Pages811-829
Number of pages19
StatePublished - Dec 1 2010
Externally publishedYes
EventInternational Congress of Mathematicians 2010, ICM 2010 - Hyderabad, India
Duration: Aug 19 2010Aug 27 2010

Publication series

NameProceedings of the International Congress of Mathematicians 2010, ICM 2010

Other

OtherInternational Congress of Mathematicians 2010, ICM 2010
CountryIndia
CityHyderabad
Period8/19/108/27/10

All Science Journal Classification (ASJC) codes

  • Mathematics(all)

Keywords

  • Ricci flow with surgery
  • Scalar curvature
  • Yamabe problem

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