MATH 668-MODERN GEOMETRY II-SPRING 2013

New source: Geometrisation of 3-manifolds, by Bessieres et al.






2/4: Bryant's steady soliton (4.6)

2/6: Classification of singularities/ parabolic rescaling/ singularity models

2/11: Perelman's no-local-collapse theorem (5.4.3)

2/13: Injectivity radius bound and singularity models (5.5.1, 5.5.2) /ruling out the cigar (5.5.3) [Brian]

Some papers on Ricci flow:

Eigenvalues and energy functionals with monotonicity formulae under Ricci flow by Jun-Fang Li (2007)

Remarks on Hamilton's compactness theorem for Ricci flow by Peter Topping (2011)
(see also Topping's web page, no. 31)

On the blow-up of four-dimensional Ricci flow singularities by Davi Maximo (2012)

Perelman's entropy functional at type I singularities of the Ricci flow by Carlo Mantegazza and Reto Mueller (2012)

Rotational symmetry of self-similar solutions to Ricci flow by Simon Brendle (2012)

Width and finite extinction time for Ricci flow by Tobias Colding and William Minicozzi II (2007)

2/18: The Hamilton-Ivey estimate in 3D

2/20: Li-Yau Harnack  estimate for positive solutions of the heat equation  (10.1)

Differential Harnack in equalities and the Ricci Flow, by Retto Mueller
found here:
reto-mueller.com/files/Mueller-DifferentialHarnack.pdf

2/25: Entropy monotonicity in the static case

2/27: Harnack inequality for the heat kernel (sign of the local entropy in static case)

3/4: Sign of local entropy, cont'd

3/6: Sign of local entropy for the backwards heat kernel (Ricci flow solution ) [Brian]

3/11: Matrix differential Harnack for positive slns of the heat eqn.

3/13: Type I blowup limits are Ricci solitons (Mantegazza-Mueller) [Caleb]