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 -