TY - GEN

T1 - Scalar curvature, conformal geometry, and the Ricci flow with surgery

AU - Marques, Fernando Coda

PY - 2010/12/1

Y1 - 2010/12/1

N2 - 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.

AB - 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.

KW - Ricci flow with surgery

KW - Scalar curvature

KW - Yamabe problem

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M3 - Conference contribution

AN - SCOPUS:84877919283

SN - 9814324302

SN - 9789814324304

T3 - Proceedings of the International Congress of Mathematicians 2010, ICM 2010

SP - 811

EP - 829

BT - Proceedings of the International Congress of Mathematicians 2010, ICM 2010

T2 - International Congress of Mathematicians 2010, ICM 2010

Y2 - 19 August 2010 through 27 August 2010

ER -