Abstract
AbstractIn this paper, we prove that any mean curvature flow translator$$\Sigma ^2 \subset {\mathbb {R}}^3$$Σ2⊂R3with finite total curvature and one end must be a plane. We also prove that if the translator$$\Sigma $$Σhas multiple ends, they are asymptotic to a plane$$\Pi $$Πcontaining the direction of translation and can be written as graphs over$$\Pi $$Π. Finally, we determine that the ends of$$\Sigma $$Σare strongly asymptotic to$$\Pi $$Πand obtain quantitative estimates for their asymptotic behavior.
Funder
College of Letters and Sciences, University of Wisconsin–Madison
Publisher
Springer Science and Business Media LLC
Subject
Applied Mathematics,Analysis
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