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Geometric flow equations

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2018

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https://doi.org/10.1007/978-3-030-01126-0_2
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Published

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CORTÉS, Vicente, ed., Klaus KRÖNCKE, ed., Jan LOUIS, ed.. Geometric flows and the geometry of space-time. Cham: Birkhäuser, 2018, pp. 77-121. Tutorials, schools, and workshops in the mathematical sciences. ISBN 978-3-030-01125-3. Available under: doi: 10.1007/978-3-030-01126-0_2

Zusammenfassung

In this minicourse, we study hypersurfaces that solve geometric evolution equations. More precisely, we investigate hypersurfaces that evolve with a normal velocity depending on a curvature function like the mean curvature or Gauß curvature. In three lectures, we address

- hypersurfaces, principal curvatures and evolution equations for geometric quantities like the metric and the second fundamental form.
- the convergence of convex hypersurfaces to round points. Here, we will also show some computer algebra calculations.
- the evolution of graphical hypersurfaces under mean curvature flow.

Zusammenfassung in einer weiteren Sprache

Fachgebiet (DDC)
510 Mathematik

Schlagwörter

mean curvature flow, geometric flow equation

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ISO 690SCHNÜRER, Oliver C., 2018. Geometric flow equations. In: CORTÉS, Vicente, ed., Klaus KRÖNCKE, ed., Jan LOUIS, ed.. Geometric flows and the geometry of space-time. Cham: Birkhäuser, 2018, pp. 77-121. Tutorials, schools, and workshops in the mathematical sciences. ISBN 978-3-030-01125-3. Available under: doi: 10.1007/978-3-030-01126-0_2
BibTex
@incollection{Schnurer2018Geome-47073,
  year={2018},
  doi={10.1007/978-3-030-01126-0_2},
  title={Geometric flow equations},
  isbn={978-3-030-01125-3},
  publisher={Birkhäuser},
  address={Cham},
  series={Tutorials, schools, and workshops in the mathematical sciences},
  booktitle={Geometric flows and the geometry of space-time},
  pages={77--121},
  editor={Cortés, Vicente and Kröncke, Klaus and Louis, Jan},
  author={Schnürer, Oliver C.}
}
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