Geometry & Topology Volume 23, issue 3 (2019)

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Sharp entropy bounds for self-shrinkers in mean curvature flow

Or Hershkovits and Brian White

Geometry & Topology 23 (2019) 1611–1619

DOI: 10.2140/gt.2019.23.1611

Bibliography

1	S B Angenent, Shrinking doughnuts, from: "Nonlinear diffusion equations and their equilibrium states, III" (editors N G Lloyd, W M Ni, L A Peletier, J Serrin), Progr. Nonlinear Differential Equations Appl. 7, Birkhäuser (1992) 21 MR1167827
2	J Bernstein, L Wang, A topological property of asymptotically conical self-shrinkers of small entropy, Duke Math. J. 166 (2017) 403 MR3606722
3	J Bernstein, L Wang, Topology of closed hypersurfaces of small entropy, Geom. Topol. 22 (2018) 1109 MR3748685
4	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
5	T H Colding, W P Minicozzi II, Generic mean curvature flow, I : Generic singularities, Ann. of Math. 175 (2012) 755 MR2993752
6	R Haslhofer, O Hershkovits, Singularities of mean convex level set flow in general ambient manifolds, Adv. Math. 329 (2018) 1137 MR3783435
7	O Hershkovits, B White, The regularity and structure theory of advancing fronts motion by mean curvature plus a forcing term, in preparation
8	O Hershkovits, B White, Avoidance for set-theoretic solutions of mean-curvature-type flows, preprint (2018) arXiv:1809.03026
9	O Hershkovits, B White, A Morse-theoretic approach to topological changes in mean curvature flow, in preparation (2018)
10	G Huisken, Asymptotic behavior for singularities of the mean curvature flow, J. Differential Geom. 31 (1990) 285 MR1030675
11	G Huisken, C Sinestrari, Convexity estimates for mean curvature flow and singularities of mean convex surfaces, Acta Math. 183 (1999) 45 MR1719551
12	T Ilmanen, The level-set flow on a manifold, from: "Differential geometry: partial differential equations on manifolds" (editor R Greene), Proc. Sympos. Pure Math. 54, Amer. Math. Soc. (1993) 193 MR1216585
13	T Ilmanen, Singularities of mean curvature flow of surfaces, preprint (1995)
14	T Ilmanen, Problems in mean curvature flow, preprint (2003)
15	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
16	D Ketover, Self-shrinking platonic solids, preprint (2016) arXiv:1602.07271
17	A Stone, A density function and the structure of singularities of the mean curvature flow, Calc. Var. Partial Differential Equations 2 (1994) 443 MR1383918
18	B White, The topology of hypersurfaces moving by mean curvature, Comm. Anal. Geom. 3 (1995) 317 MR1362655
19	B White, Stratification of minimal surfaces, mean curvature flows, and harmonic maps, J. Reine Angew. Math. 488 (1997) 1 MR1465365
20	B White, The size of the singular set in mean curvature flow of mean-convex sets, J. Amer. Math. Soc. 13 (2000) 665 MR1758759
21	B White, The nature of singularities in mean curvature flow of mean-convex sets, J. Amer. Math. Soc. 16 (2003) 123 MR1937202
22	B White, Topological change in mean convex mean curvature flow, Invent. Math. 191 (2013) 501 MR3020169
23	B White, Subsequent singularities in mean-convex mean curvature flow, Calc. Var. Partial Differential Equations 54 (2015) 1457 MR3396419