TY - JOUR

T1 - Singularities of mean convex level set flow in general ambient manifolds

AU - Haslhofer, Robert

AU - Hershkovits, Or

N1 - Publisher Copyright:
© 2018 Elsevier Inc.

PY - 2018/4/30

Y1 - 2018/4/30

N2 - We prove two new estimates for the level set flow of mean convex domains in Riemannian manifolds. Our estimates give control – exponential in time – for the infimum of the mean curvature, and the ratio between the norm of the second fundamental form and the mean curvature. In particular, the estimates remove a stumbling block that has been left after the work of White [16,17,20], and Haslhofer–Kleiner [9], and thus allow us to extend the structure theory for mean convex level set flow to general ambient manifolds of arbitrary dimension.

AB - We prove two new estimates for the level set flow of mean convex domains in Riemannian manifolds. Our estimates give control – exponential in time – for the infimum of the mean curvature, and the ratio between the norm of the second fundamental form and the mean curvature. In particular, the estimates remove a stumbling block that has been left after the work of White [16,17,20], and Haslhofer–Kleiner [9], and thus allow us to extend the structure theory for mean convex level set flow to general ambient manifolds of arbitrary dimension.

KW - Level set flow

KW - Mean curvature flow

UR - http://www.scopus.com/inward/record.url?scp=85042920043&partnerID=8YFLogxK

U2 - 10.1016/j.aim.2018.02.008

DO - 10.1016/j.aim.2018.02.008

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AN - SCOPUS:85042920043

SN - 0001-8708

VL - 329

SP - 1137

EP - 1155

JO - Advances in Mathematics

JF - Advances in Mathematics

ER -