Download this article
 Download this article For screen
For printing
Recent Issues

Volume 30
Issue 4, 1203–1610
Issue 3, 835–1201
Issue 2, 389–833
Issue 1, 1–388

Volume 29, 9 issues

Volume 28, 9 issues

Volume 27, 9 issues

Volume 26, 8 issues

Volume 25, 7 issues

Volume 24, 7 issues

Volume 23, 7 issues

Volume 22, 7 issues

Volume 21, 6 issues

Volume 20, 6 issues

Volume 19, 6 issues

Volume 18, 5 issues

Volume 17, 5 issues

Volume 16, 4 issues

Volume 15, 4 issues

Volume 14, 5 issues

Volume 13, 5 issues

Volume 12, 5 issues

Volume 11, 4 issues

Volume 10, 4 issues

Volume 9, 4 issues

Volume 8, 3 issues

Volume 7, 2 issues

Volume 6, 2 issues

Volume 5, 2 issues

Volume 4, 1 issue

Volume 3, 1 issue

Volume 2, 1 issue

Volume 1, 1 issue

The Journal
About the journal
Ethics and policies
Peer-review process
 
Submission guidelines
Submission form
Editorial board
 
Subscriptions
 
ISSN (electronic): 1364-0380
ISSN (print): 1465-3060
 
Author index
To appear
 
Other MSP journals
Closed Ricci flows with singularities modeled on asymptotically conical shrinkers

Maxwell Stolarski

Geometry & Topology 30 (2026) 1277–1370
DOI: 10.2140/gt.2026.30.1277
Bibliography
1 F J Almgren Jr., Dirichlet’s problem for multiple valued functions and the regularity of mass minimizing integral currents, from: "Minimal submanifolds and geodesics" (editor M Obata), North-Holland (1979) 1 MR574247
2 S Angenent, D Knopf, An example of neckpinching for Ricci flow on Sn+1, Math. Res. Lett. 11 (2004) 493 MR2092903
3 S B Angenent, D Knopf, Ricci solitons, conical singularities, and nonuniqueness, Geom. Funct. Anal. 32 (2022) 411 MR4431121
4 S B Angenent, J J L Velázquez, Degenerate neckpinches in mean curvature flow, J. Reine Angew. Math. 482 (1997) 15 MR1427656
5 S B Angenent, J Isenberg, D Knopf, Degenerate neckpinches in Ricci flow, J. Reine Angew. Math. 709 (2015) 81 MR3430876
6 S Angenent, T Ilmanen, J J Velázquez, Fattening from smooth initial data in mean curvature flow, in preparation
7 A Appleton, Scalar curvature rigidity and Ricci DeTurck flow on perturbations of Euclidean space, Calc. Var. Partial Differential Equations 57 (2018) 132 MR3844513
8 A Appleton, Eguchi–Hanson singularities in U(2)-invariant Ricci flow, Peking Math. J. 6 (2023) 1 MR4552641
9 T Aubin, Some nonlinear problems in Riemannian geometry, Springer (1998) MR1636569
10 R H Bamler, Stability of hyperbolic manifolds with cusps under Ricci flow, Adv. Math. 263 (2014) 412 MR3239144
11 R H Bamler, Structure theory of non-collapsed limits of Ricci flows, (2020) arXiv:2009.03243
12 R H Bamler, B Kleiner, Uniqueness and stability of Ricci flow through singularities, Acta Math. 228 (2022) 1 MR4448680
13 J Bernstein, Asymptotic structure of almost eigenfunctions of drift Laplacians on conical ends, Amer. J. Math. 142 (2020) 1897 MR4176548
14 P Biernat, Y Seki, Type II blow-up mechanism for supercritical harmonic map heat flow, Int. Math. Res. Not. 2019 (2019) 407 MR3903563
15 H D Cao, D Zhou, On complete gradient shrinking Ricci solitons, J. Differential Geom. 85 (2010) 175 MR2732975
16 B L Chen, Strong uniqueness of the Ricci flow, J. Differential Geom. 82 (2009) 363 MR2520796
17 B L Chen, X P Zhu, Uniqueness of the Ricci flow on complete noncompact manifolds, J. Differential Geom. 74 (2006) 119 MR2260930
18 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, I : Geometric aspects, 135, Amer. Math. Soc. (2007) MR2302600
19 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, III : Geometric-analytic aspects, 163, Amer. Math. Soc. (2010) MR2604955
20 T H Colding, W P Minicozzi, Optimal growth bounds for eigenfunctions, (2021) arXiv:2109.04998
21 A S Dancer, M Y Wang, On Ricci solitons of cohomogeneity one, Ann. Global Anal. Geom. 39 (2011) 259 MR2769300
22 A Deruelle, F Schulze, A relative entropy and a unique continuation result for Ricci expanders, Comm. Pure Appl. Math. 76 (2023) 2613 MR4630599
23 F Di Giovanni, Ricci flow of warped Berger metrics on 4, Calc. Var. Partial Differential Equations 59 (2020) 162 MR4149338
24 J Enders, R Müller, P M Topping, On type-I singularities in Ricci flow, Comm. Anal. Geom. 19 (2011) 905 MR2886712
25 M Feldman, T Ilmanen, D Knopf, Rotationally symmetric shrinking and expanding gradient Kähler–Ricci solitons, J. Differential Geom. 65 (2003) 169 MR2058261
26 A Grigor’yan, Heat kernel and analysis on manifolds, 47, Amer. Math. Soc. (2009) MR2569498
27 R S Hamilton, The formation of singularities in the Ricci flow, from: "Surveys in differential geometry, II" (editors C C Hsiung, S T Yau), Int. (1995) 7 MR1375255
28 M Herrero, J Velázquez, A blow-up result for semilinear heat equations in the supercritical case, unpublished preprint
29 T Ilmanen, B White, Fattening in mean curvature flow, Ars Inven. Anal. (2025) 4 MR4888468
30 B Kotschwar, L Wang, Rigidity of asymptotically conical shrinking gradient Ricci solitons, J. Differential Geom. 100 (2015) 55 MR3326574
31 N V Krylov, Lectures on elliptic and parabolic equations in Hölder spaces, 12, Amer. Math. Soc. (1996) MR1406091
32 T K Lee, X Zhao, Closed mean curvature flows with asymptotically conical singularities, (2024) arXiv:2405.15577
33 P Lu, A local curvature bound in Ricci flow, Geom. Topol. 14 (2010) 1095 MR2629901
34 D Máximo, On the blow-up of four-dimensional Ricci flow singularities, J. Reine Angew. Math. 692 (2014) 153 MR3274550
35 N Mizoguchi, Type-II blowup for a semilinear heat equation, Adv. Differential Equations 9 (2004) 1279 MR2099557
36 O Munteanu, J Wang, Conical structure for shrinking Ricci solitons, J. Eur. Math. Soc. (JEMS) 19 (2017) 3377 MR3713043
37 G Perelman, The entropy formula for the Ricci flow and its geometric applications, (2002) arXiv:math/0211159
38 M Reed, B Simon, Methods of modern mathematical physics, IV : Analysis of operators, Academic (1978) MR493421
39 W X Shi, Deforming the metric on complete Riemannian manifolds, J. Differential Geom. 30 (1989) 223 MR1001277
40 M Stolarski, Curvature blow-up in doubly-warped product metrics evolving by Ricci flow, 1470, Amer. Math. Soc. (2024) MR4726955
41 J J L Velázquez, Curvature blow-up in perturbations of minimal cones evolving by mean curvature flow, Ann. Scuola Norm. Sup. Pisa Cl. Sci. (4) 21 (1994) 595 MR1318773
42 T Ważewski, Sur un principe topologique de l’examen de l’allure asymptotique des intégrales des équations différentielles ordinaires, Ann. Soc. Polon. Math. 20 (1947) 279 MR26206
43 H Wu, On type-II singularities in Ricci flow on N, Comm. Partial Differential Equations 39 (2014) 2064 MR3251864
44 Z H Zhang, On the completeness of gradient Ricci solitons, Proc. Amer. Math. Soc. 137 (2009) 2755 MR2497489