Geometry & Topology Volume 22, issue 2 (2018)

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ISSN (electronic): 1364-0380

ISSN (print): 1465-3060

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Topology of closed hypersurfaces of small entropy

Jacob Bernstein and Lu Wang

Geometry & Topology 22 (2018) 1109–1141

DOI: 10.2140/gt.2018.22.1109

Bibliography

1	J W Alexander, On the subdivision of 3–space by a polyhedron, Nat. Acad. Proc. 10 (1924) 6
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	K A Brakke, The motion of a surface by its mean curvature, 20, Princeton Univ. Press (1978) MR485012
5	J Cerf, Sur les difféomorphismes de la sphère de dimension trois (Γ₄ = 0), 53, Springer (1968) MR0229250
6	Y G Chen, Y Giga, S Goto, Uniqueness and existence of viscosity solutions of generalized mean curvature flow equations, J. Differential Geom. 33 (1991) 749 MR1100211
7	X Cheng, D Zhou, Volume estimate about shrinkers, Proc. Amer. Math. Soc. 141 (2013) 687 MR2996973
8	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
9	T H Colding, W P Minicozzi II, Generic mean curvature flow, I : Generic singularities, Ann. of Math. 175 (2012) 755 MR2993752
10	L C Evans, J Spruck, Motion of level sets by mean curvature, I, J. Differential Geom. 33 (1991) 635 MR1100206
11	L C Evans, J Spruck, Motion of level sets by mean curvature, II, Trans. Amer. Math. Soc. 330 (1992) 321 MR1068927
12	L C Evans, J Spruck, Motion of level sets by mean curvature, III, J. Geom. Anal. 2 (1992) 121 MR1151756
13	L C Evans, J Spruck, Motion of level sets by mean curvature, IV, J. Geom. Anal. 5 (1995) 77 MR1315658
14	M W Hirsch, Differential topology, 33, Springer (1976) MR0448362
15	W Y Hsiang, Minimal cones and the spherical Bernstein problem, I, Ann. of Math. 118 (1983) 61 MR707161
16	W Y Hsiang, Minimal cones and the spherical Bernstein problem, II, Invent. Math. 74 (1983) 351 MR724010
17	W Y Hsiang, I Sterling, Minimal cones and the spherical Bernstein problem, III, Invent. Math. 85 (1986) 223 MR846927
18	G Huisken, Flow by mean curvature of convex surfaces into spheres, J. Differential Geom. 20 (1984) 237 MR772132
19	G Huisken, Asymptotic behavior for singularities of the mean curvature flow, J. Differential Geom. 31 (1990) 285 MR1030675
20	T Ilmanen, Elliptic regularization and partial regularity for motion by mean curvature, 520, Amer. Math. Soc. (1994) MR1196160
21	T Ilmanen, Singularities of mean curvature flow of surfaces, preprint (1995)
22	T Ilmanen, A Neves, F Schulze, On short time existence for the planar network flow, preprint (2014) arXiv:1407.4756
23	T Ilmanen, B White, Sharp lower bounds on density for area-minimizing cones, Camb. J. Math. 3 (2015) 1 MR3356355
24	D Ketover, X Zhou, Entropy of closed surfaces and min-max theory, preprint (2015) arXiv:1509.06238
25	F C Marques, A Neves, Min-max theory and the Willmore conjecture, Ann. of Math. 179 (2014) 683 MR3152944
26	J Munkres, Differentiable isotopies on the 2–sphere, Michigan Math. J. 7 (1960) 193 MR0144354
27	S Osher, J A Sethian, Fronts propagating with curvature-dependent speed : algorithms based on Hamilton–Jacobi formulations, J. Comput. Phys. 79 (1988) 12 MR965860
28	F Schulze, Uniqueness of compact tangent flows in mean curvature flow, J. Reine Angew. Math. 690 (2014) 163 MR3200339
29	L Simon, Lectures on geometric measure theory, 3, Aust. Nat. Univ., Centre for Math. Anal. (1983) MR756417
30	S Smale, Diffeomorphisms of the 2–sphere, Proc. Amer. Math. Soc. 10 (1959) 621 MR0112149
31	A Stone, A density function and the structure of singularities of the mean curvature flow, Calc. Var. Partial Differential Equations 2 (1994) 443 MR1383918
32	L Wang, Uniqueness of self-similar shrinkers with asymptotically conical ends, J. Amer. Math. Soc. 27 (2014) 613 MR3194490
33	B White, A local regularity theorem for mean curvature flow, Ann. of Math. 161 (2005) 1487 MR2180405
34	J J Zhu, On the entropy of closed hypersurfaces and singular self-shrinkers, preprint (2016) arXiv:1607.07760