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

Volume 30
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
A nonexistence result for wing-like mean curvature flows in $\mathbb{R}^4$

Kyeongsu Choi, Robert Haslhofer and Or Hershkovits

Geometry & Topology 28 (2024) 3095–3134
Bibliography
1 S J Altschuler, L F Wu, Translating surfaces of the non-parametric mean curvature flow with prescribed contact angle, Calc. Var. Partial Differential Equations 2 (1994) 101 MR1384396
2 B Andrews, Noncollapsing in mean-convex mean curvature flow, Geom. Topol. 16 (2012) 1413 MR2967056
3 S Angenent, P Daskalopoulos, N Sesum, Unique asymptotics of ancient convex mean curvature flow solutions, J. Differential Geom. 111 (2019) 381 MR3934596
4 S Angenent, P Daskalopoulos, N Sesum, Uniqueness of two-convex closed ancient solutions to the mean curvature flow, Ann. of Math. 192 (2020) 353 MR4151080
5 S Brendle, A sharp bound for the inscribed radius under mean curvature flow, Invent. Math. 202 (2015) 217 MR3402798
6 S Brendle, K Choi, Uniqueness of convex ancient solutions to mean curvature flow in 3, Invent. Math. 217 (2019) 35 MR3958790
7 S Brendle, K Choi, Uniqueness of convex ancient solutions to mean curvature flow in higher dimensions, Geom. Topol. 25 (2021) 2195 MR4310889
8 S Brendle, G Huisken, Mean curvature flow with surgery of mean convex surfaces in 3, Invent. Math. 203 (2016) 615 MR3455158
9 J Cheeger, R Haslhofer, A Naber, Quantitative stratification and the regularity of mean curvature flow, Geom. Funct. Anal. 23 (2013) 828 MR3061773
10 K Choi, R Haslhofer, O Hershkovits, Ancient low-entropy flows, mean-convex neighborhoods, and uniqueness, Acta Math. 228 (2022) 217 MR4448681
11 K Choi, R Haslhofer, O Hershkovits, B White, Ancient asymptotically cylindrical flows and applications, Invent. Math. 229 (2022) 139 MR4438354
12 K Choi, C Mantoulidis, Ancient gradient flows of elliptic functionals and Morse index, Amer. J. Math. 144 (2022) 541 MR4401511
13 T H Colding, W P Minicozzi II, Generic mean curvature flow, I : Generic singularities, Ann. of Math. 175 (2012) 755 MR2993752
14 T H Colding, W P Minicozzi II, Uniqueness of blowups and Łojasiewicz inequalities, Ann. of Math. 182 (2015) 221 MR3374960
15 T H Colding, W P Minicozzi II, The singular set of mean curvature flow with generic singularities, Invent. Math. 204 (2016) 443 MR3489702
16 R Haslhofer, B Kleiner, On Brendle’s estimate for the inscribed radius under mean curvature flow, Int. Math. Res. Not. 2015 (2015) 6558 MR3384488
17 R Haslhofer, B Kleiner, Mean curvature flow of mean convex hypersurfaces, Comm. Pure Appl. Math. 70 (2017) 511 MR3602529
18 R Haslhofer, B Kleiner, Mean curvature flow with surgery, Duke Math. J. 166 (2017) 1591 MR3662439
19 D Hoffman, T Ilmanen, F Martín, B White, Graphical translators for mean curvature flow, Calc. Var. Partial Differential Equations 58 (2019) 117 MR3962912
20 G Huisken, Asymptotic behavior for singularities of the mean curvature flow, J. Differential Geom. 31 (1990) 285 MR1030675
21 G Huisken, Local and global behaviour of hypersurfaces moving by mean curvature, from: "Differential geometry: partial differential equations on manifolds" (editors R Greene, S T Yau), Proc. Sympos. Pure Math. 54.1, Amer. Math. Soc. (1993) 175 MR1216584
22 G Huisken, C Sinestrari, Mean curvature flow with surgeries of two-convex hypersurfaces, Invent. Math. 175 (2009) 137 MR2461428
23 T Ilmanen, Singularities of mean curvature flow of surfaces, preprint (1995)
24 S Kleene, N M Møller, Self-shrinkers with a rotational symmetry, Trans. Amer. Math. Soc. 366 (2014) 3943 MR3206448
25 G M Lieberman, Second order parabolic differential equations, World Sci. (1996) MR1465184
26 F Merle, H Zaag, Optimal estimates for blowup rate and behavior for nonlinear heat equations, Comm. Pure Appl. Math. 51 (1998) 139 MR1488298
27 W Sheng, X J Wang, Singularity profile in the mean curvature flow, Methods Appl. Anal. 16 (2009) 139 MR2563745
28 J Spruck, L Xiao, Complete translating solitons to the mean curvature flow in 3 with nonnegative mean curvature, Amer. J. Math. 142 (2020) 993 MR4101337
29 X J Wang, Convex solutions to the mean curvature flow, Ann. of Math. 173 (2011) 1185 MR2800714
30 B White, The size of the singular set in mean curvature flow of mean-convex sets, J. Amer. Math. Soc. 13 (2000) 665 MR1758759
31 B White, The nature of singularities in mean curvature flow of mean-convex sets, J. Amer. Math. Soc. 16 (2003) 123 MR1937202