@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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    <dc:contributor>Maurer, Wolfgang</dc:contributor>
    <dcterms:title>Shadows of graphical mean curvature flow</dcterms:title>
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    <dcterms:abstract xml:lang="eng">We consider mean curvature flow of an initial surface that is the graph of a function over some domain of definition in R&lt;sup&gt;n&lt;/sup&gt;. 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 R&lt;sup&gt;n&lt;/sup&gt;, the shadow of the flow. This moving shadow can be seen as a weak solution for mean curvature flow of hypersurfaces in R&lt;sup&gt;n&lt;/sup&gt; 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.</dcterms:abstract>
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    <dc:creator>Maurer, Wolfgang</dc:creator>
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