Shadows of graphical mean curvature flow

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We consider mean curvature flow of an initial surface that is the graph of a function over some domain of definition in Rn. If the graph is not complete then we impose a constant Dirichlet boundary condition at the boundary of the surface.We establish longtime-existence of the flow and investigate the projection of the flowing surface onto Rn, the shadow of the flow. This moving shadow can be seen as a weak solution for mean curvature flow of hypersurfaces in Rn with a Dirichlet boundary condition. Furthermore, we provide a lemma of independent interest to locally mollify the boundary of an intersection of two smooth open sets in a way that respects curvature conditions.

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ISO 690MAURER, Wolfgang, 2021. Shadows of graphical mean curvature flow. In: Communications in Analysis and Geometry. International Press. 2021, 29(1), pp. 183-206. ISSN 1019-8385. eISSN 1944-9992. Available under: doi: 10.4310/CAG.2021.v29.n1.a6
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@article{Maurer2021Shado-53443,
  year={2021},
  doi={10.4310/CAG.2021.v29.n1.a6},
  title={Shadows of graphical mean curvature flow},
  number={1},
  volume={29},
  issn={1019-8385},
  journal={Communications in Analysis and Geometry},
  pages={183--206},
  author={Maurer, Wolfgang}
}
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