Geometry & Topology Volume 25, issue 2 (2021)

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Local mollification of Riemannian metrics using Ricci flow, and Ricci limit spaces

Miles Simon and Peter M Topping

Geometry & Topology 25 (2021) 913–948

DOI: 10.2140/gt.2021.25.913

Bibliography

1	M T Anderson, Degeneration of metrics with bounded curvature and applications to critical metrics of Riemannian functionals, from: "Differential geometry : Riemannian geometry" (editors R Greene, S T Yau), Proc. Sympos. Pure Math. 54, Amer. Math. Soc. (1993) 53 MR1216611
2	R H Bamler, E Cabezas-Rivas, B Wilking, The Ricci flow under almost non-negative curvature conditions, Invent. Math. 217 (2019) 95 MR3958792
3	C Böhm, B Wilking, Manifolds with positive curvature operators are space forms, Ann. of Math. 167 (2008) 1079 MR2415394
4	S Brendle, R Schoen, Manifolds with 1∕4–pinched curvature are space forms, J. Amer. Math. Soc. 22 (2009) 287 MR2449060
5	D Burago, Y Burago, S Ivanov, A course in metric geometry, 33, Amer. Math. Soc. (2001) MR1835418
6	J Cheeger, Degeneration of Riemannian metrics under Ricci curvature bounds, Scuola Normale Superiore (2001) MR2006642
7	J Cheeger, T H Colding, On the structure of spaces with Ricci curvature bounded below, I, J. Differential Geom. 46 (1997) 406 MR1484888
8	J Cheeger, T H Colding, G Tian, On the singularities of spaces with bounded Ricci curvature, Geom. Funct. Anal. 12 (2002) 873 MR1937830
9	J Cheeger, M Gromov, M Taylor, Finite propagation speed, kernel estimates for functions of the Laplace operator, and the geometry of complete Riemannian manifolds, J. Differential Geom. 17 (1982) 15 MR658471
10	B L Chen, Strong uniqueness of the Ricci flow, J. Differential Geom. 82 (2009) 363 MR2520796
11	B Chow, S C Chu, D Glickenstein, C Guenther, J Isenberg, T Ivey, D Knopf, P Lu, F Luo, L Ni, The Ricci flow : techniques and applications, II : Analytic aspects, 144, Amer. Math. Soc. (2008) MR2365237
12	B Chow, P Lu, L Ni, Hamilton’s Ricci flow, 77, Amer. Math. Soc. (2006) MR2274812
13	P Gianniotis, The Ricci flow on manifolds with boundary, J. Differential Geom. 104 (2016) 291 MR3557306
14	R S Hamilton, Three-manifolds with positive Ricci curvature, J. Differential Geom. 17 (1982) 255 MR664497
15	R Hochard, Short-time existence of the Ricci flow on complete, non-collapsed 3–manifolds with Ricci curvature bounded from below, preprint (2016) arXiv:1603.08726
16	R Hochard, Théorèmes d’existence en temps court du flot de Ricci pour des variétés non-complètes, non-éffondrées, à courbure minorée, PhD thesis, Université de Bordeaux (2019)
17	Y Lai, Ricci flow under local almost non-negative curvature conditions, Adv. Math. 343 (2019) 353 MR3881661
18	M C Lee, L F Tam, Chern–Ricci flows on noncompact complex manifolds, J. Differential Geom. 115 (2020) 529 MR4120818
19	A D McLeod, P M Topping, Global regularity of three-dimensional Ricci limit spaces, preprint (2018) arXiv:1803.00414
20	A D McLeod, P M Topping, Pyramid Ricci flow in higher dimensions, Math. Z. 296 (2020) 511 MR4140751
21	G Perelman, The entropy formula for the Ricci flow and its geometric applications, preprint (2002) arXiv:math/0211159
22	M Simon, Local results for flows whose speed or height is bounded by c∕t, Int. Math. Res. Not. 2008 (2008) MR2439551
23	M Simon, Ricci flow of non-collapsed three manifolds whose Ricci curvature is bounded from below, J. Reine Angew. Math. 662 (2012) 59 MR2876261
24	M Simon, P M Topping, Local control on the geometry in 3D Ricci flow, preprint (2016) arXiv:1611.06137
25	P Topping, Ricci flow compactness via pseudolocality, and flows with incomplete initial metrics, J. Eur. Math. Soc. 12 (2010) 1429 MR2734348
26	P M Topping, Ricci flow and Ricci limit spaces, from: "Geometric analysis" (editors M J Gursky, A Malchiodi), Lecture Notes in Math. 2263, Springer (2020) 79
27	D Yang, Convergence of Riemannian manifolds with integral bounds on curvature, I, Ann. Sci. École Norm. Sup. 25 (1992) 77 MR1152614