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Uniqueness of instantaneously complete Ricci flows

Peter M Topping

Geometry & Topology 19 (2015) 1477–1492
Bibliography
1 P Albin, C L Aldana, F Rochon, Ricci flow and the determinant of the Laplacian on non-compact surfaces, Comm. PDE 38 (2013) 711 MR3040681
2 B L Chen, Strong uniqueness of the Ricci flow, J. Differential Geom. 82 (2009) 363 MR2520796
3 B L Chen, X P Zhu, Uniqueness of the Ricci flow on complete noncompact manifolds, J. Differential Geom. 74 (2006) 119 MR2260930
4 B Chow, The Ricci flow on the $2$–sphere, J. Differential Geom. 33 (1991) 325 MR1094458
5 M R R Coffey, Ricci flow and metric geometry, PhD thesis, University of Warwick (2015)
6 P Daskalopoulos, C E Kenig, Degenerate diffusions, EMS Tracts in Mathematics 1, Eur. Math. Soc. (2007) MR2338118
7 P Daskalopoulos, M A del Pino, On a singular diffusion equation, Comm. Anal. Geom. 3 (1995) 523 MR1371208
8 D DeTurck, Collected papers on Ricci flow, Series in Geometry and Topology 37, International Press (2003) MR2145154
9 E DiBenedetto, D J Diller, About a singular parabolic equation arising in thin film dynamics and in the Ricci flow for complete $\mathbf{R}^2$, from: "Partial differential equations and applications", Lecture Notes in Pure and Appl. Math. 177, Dekker (1996) 103 MR1371583
10 G Giesen, Instantaneously complete Ricci flows on surfaces, PhD thesis, University of Warwick (2012)
11 G Giesen, P M Topping, Ricci flow of negatively curved incomplete surfaces, Calc. Var. Partial Differential Equations 38 (2010) 357 MR2647124
12 G Giesen, P M Topping, Existence of Ricci flows of incomplete surfaces, Comm. Partial Differential Equations 36 (2011) 1860 MR2832165
13 G Giesen, P M Topping, Ricci flows with unbounded curvature, Math. Z. 273 (2013) 449 MR3010170
14 G Giesen, P M Topping, Ricci flows with bursts of unbounded curvature, (2014) arXiv:1302.5686
15 R S Hamilton, Three-manifolds with positive Ricci curvature, J. Differential Geom. 17 (1982) 255 MR664497
16 R S Hamilton, The Ricci flow on surfaces, from: "Mathematics and general relativity", Contemp. Math. 71, Amer. Math. Soc. (1988) 237 MR954419
17 R S Hamilton, The formation of singularities in the Ricci flow, from: "Proc. Conf. Geometry and Topology", Surveys in Differential Geometry 2, Int. Press (1995) 7 MR1375255
18 L Ji, R Mazzeo, N Sesum, Ricci flow on surfaces with cusps, Math. Ann. 345 (2009) 819 MR2545867
19 B Kotschwar, An energy approach to the problem of uniqueness for the Ricci flow, Comm. Anal. Geom. 22 (2014) 149 MR3194377
20 G Perelman, The entropy formula for the Ricci flow and its geometric applications, arXiv:0211159v1
21 T Richard, Canonical smoothing of compact Alexandrov surfaces via Ricci flow, (2012) arXiv:1204.5461
22 A Rodriguez, J L Vazquez, J R Esteban, The maximal solution of the logarithmic fast diffusion equation in two space dimensions, Adv. Differential Equations 2 (1997) 867 MR1606339
23 W X Shi, Deforming the metric on complete Riemannian manifolds, J. Differential Geom. 30 (1989) 223 MR1001277
24 P M Topping, Ricci flow compactness via pseudolocality, and flows with incomplete initial metrics, J. Eur. Math. Soc. 12 (2010) 1429 MR2734348
25 P M Topping, Uniqueness and nonuniqueness for Ricci flow on surfaces: Reverse cusp singularities, Int. Math. Res. Not. 2012 (2012) 2356 MR2923169
26 P M Topping, Remarks on Hamilton's compactness theorem for Ricci flow, J. Reine Angew. Math. 692 (2014) 173
27 J L Vázquez, Smoothing and decay estimates for nonlinear diffusion equations, Oxford Lecture Series Math. Appl. 33, Oxford University Press (2006) MR2282669
28 S T Yau, Remarks on conformal transformations, J. Differential Geometry 8 (1973) 369 MR0339007