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On self-shrinkers of medium entropy in $\mathbb{R}^4$

Alexander Mramor

Geometry & Topology 27 (2023) 3715–3731
Bibliography
1 B Andrews, Noncollapsing in mean-convex mean curvature flow, Geom. Topol. 16 (2012) 1413 MR2967056
2 J Bernstein, L Wang, A sharp lower bound for the entropy of closed hypersurfaces up to dimension six, Invent. Math. 206 (2016) 601 MR3573969
3 J Bernstein, L Wang, A topological property of asymptotically conical self-shrinkers of small entropy, Duke Math. J. 166 (2017) 403 MR3606722
4 J Bernstein, L Wang, Topology of closed hypersurfaces of small entropy, Geom. Topol. 22 (2018) 1109 MR3748685
5 S Brendle, G Huisken, Mean curvature flow with surgery of mean convex surfaces in 3, Invent. Math. 203 (2016) 615 MR3455158
6 B L Chen, L Yin, Uniqueness and pseudolocality theorems of the mean curvature flow, Comm. Anal. Geom. 15 (2007) 435 MR2379801
7 O Chodosh, K Choi, C Mantoulidis, F Schulze, Mean curvature flow with generic initial data, preprint (2020) arXiv:2003.14344
8 O Chodosh, K Choi, C Mantoulidis, F Schulze, Mean curvature flow with generic low-entropy initial data, preprint (2021) arXiv:2102.11978
9 T H Colding, T Ilmanen, W P Minicozzi II, B White, The round sphere minimizes entropy among closed self-shrinkers, J. Differential Geom. 95 (2013) 53 MR3128979
10 T H Colding, W P Minicozzi II, Generic mean curvature flow, I : Generic singularities, Ann. of Math. 175 (2012) 755 MR2993752
11 T H Colding, W P Minicozzi II, Smooth compactness of self-shrinkers, Comment. Math. Helv. 87 (2012) 463 MR2914856
12 J M Daniels-Holgate, Approximation of mean curvature flow with generic singularities by smooth flows with surgery, Adv. Math. 410 (2022) 108715 MR4493003
13 Q Ding, Y L Xin, Volume growth, eigenvalue and compactness for self-shrinkers, Asian J. Math. 17 (2013) 443 MR3119795
14 M H Freedman, The topology of four-dimensional manifolds, J. Differential Geometry 17 (1982) 357 MR0679066
15 R Haslhofer, D Ketover, Minimal 2–spheres in 3–spheres, Duke Math. J. 168 (2019) 1929 MR3983295
16 R Haslhofer, B Kleiner, Mean curvature flow of mean convex hypersurfaces, Comm. Pure Appl. Math. 70 (2017) 511 MR3602529
17 R Haslhofer, B Kleiner, Mean curvature flow with surgery, Duke Math. J. 166 (2017) 1591 MR3662439
18 A Hatcher, Notes on basic 3–manifold topology, unpublished manuscript (2007)
19 J Head, The surgery and level-set approaches to mean curvature flow, PhD thesis, Max Planck Institute for Gravitational Physics (2011)
20 J Head, On the mean curvature evolution of two-convex hypersurfaces, J. Differential Geom. 94 (2013) 241 MR3080482
21 O Hershkovits, B White, Sharp entropy bounds for self-shrinkers in mean curvature flow, Geom. Topol. 23 (2019) 1611 MR3956898
22 G Huisken, Asymptotic behavior for singularities of the mean curvature flow, J. Differential Geom. 31 (1990) 285 MR1030675
23 G Huisken, C Sinestrari, Mean curvature flow with surgeries of two-convex hypersurfaces, Invent. Math. 175 (2009) 137 MR2461428
24 T Ilmanen, B White, Sharp lower bounds on density for area-minimizing cones, Camb. J. Math. 3 (2015) 1 MR3356355
25 N Kapouleas, S J Kleene, N M Møller, Mean curvature self-shrinkers of high genus: non-compact examples, J. Reine Angew. Math. 739 (2018) 1 MR3808256
26 J Lauer, Convergence of mean curvature flows with surgery, Comm. Anal. Geom. 21 (2013) 355 MR3043750
27 J M Lee, Introduction to smooth manifolds, 218, Springer (2013) MR2954043
28 A Mramor, An unknottedness result for noncompact self shrinkers, preprint (2020) arXiv:2005.01688
29 A Mramor, S Wang, Low entropy and the mean curvature flow with surgery, Calc. Var. Partial Differential Equations 60 (2021) 96 MR4249874
30 G Perelman, The entropy formula for the Ricci flow and its geometric applications, preprint (2002) arXiv:math/0211159
31 G Perelman, Finite extinction time for the solutions to the Ricci flow on certain three-manifolds, preprint (2003) arXiv:math/0307245
32 G Perelman, Ricci flow with surgery on three-manifolds, preprint (2003) arXiv:math/0303109
33 S Smale, Generalized Poincaré’s conjecture in dimensions greater than four, Ann. of Math. 74 (1961) 391 MR0137124
34 A Stone, A density function and the structure of singularities of the mean curvature flow, Calc. Var. Partial Differential Equations 2 (1994) 443 MR1383918
35 L Wang, Asymptotic structure of self-shrinkers, preprint (2016) arXiv:1610.04904
36 L Wang, Uniqueness of self-similar shrinkers with asymptotically cylindrical ends, J. Reine Angew. Math. 715 (2016) 207 MR3507924
37 B White, Stratification of minimal surfaces, mean curvature flows, and harmonic maps, J. Reine Angew. Math. 488 (1997) 1 MR1465365
38 B White, The size of the singular set in mean curvature flow of mean-convex sets, J. Amer. Math. Soc. 13 (2000) 665 MR1758759
39 B White, Topological change in mean convex mean curvature flow, Invent. Math. 191 (2013) 501 MR3020169