Topological uniqueness for self-expanders of small entropy
J Bernstein, L Wang - arXiv preprint arXiv:1902.02642, 2019 - arxiv.org
J Bernstein, L Wang
arXiv preprint arXiv:1902.02642, 2019•arxiv.org… [1]), we showed that there is an open subset in the space of regular cones in R3 so that
for any cone in the subset there are at least three distinct self-expanders asymptotic to the
cone – two that are topologically annuli and one that is a pair of disks. Our main result is that
this topological non-uniqueness cannot occur for self-expanders that are asymptotic to a
low entropy cone. … We prove existence and topological uniqueness results for
asymptotically conical self-expanders with asymptotic link in S …
for any cone in the subset there are at least three distinct self-expanders asymptotic to the
cone – two that are topologically annuli and one that is a pair of disks. Our main result is that
this topological non-uniqueness cannot occur for self-expanders that are asymptotic to a
low entropy cone. … We prove existence and topological uniqueness results for
asymptotically conical self-expanders with asymptotic link in S …
For a fixed regular cone in Euclidean space with small entropy we show that all smooth self-expanding solutions of the mean curvature flow that are asymptotic to the cone are in the same isotopy class.
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