Finite topology self-translating surfaces for the mean curvature flow in $\mathbb R^3$

  title={Finite topology self-translating surfaces for the mean curvature flow in \$\mathbb R^3\$},
  author={Juan D{\'a}vila and Manuel del Pino and Xu{\^a}n Hi{\^e}n Nguy{\^e}n},
  journal={arXiv: Analysis of PDEs},
Finite topology self translating surfaces to mean curvature flow of surfaces constitute a key element for the analysis of Type II singularities from a compact surface, since they arise in a limit after suitable blow-up scalings around the singularity. We find in $\mathbb R^3$ a surface $M$ orientable, embedded and complete with finite topology (and large genus) with three ends asymptotically paraboloidal, such that the moving surface $\Sigma(t) = M + te_z$ evolves by mean curvature flow. This… Expand
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