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Non-parametric radially symmetric mean curvature flow with a free boundary

Journal Article


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Abstract


  • We study the mean curvature flow of radially symmetric graphs with prescribed contact angle on a fixed, smooth hypersurface in Euclidean space. In this paper we treat two distinct problems. The first problem has a free Neumann boundary only, while the second has two disjoint boundaries, a free Neumann boundary and a fixed Dirichlet height. We separate the two problems and prove that under certain initial conditions we have either long time existence followed by convergence to a minimal surface, or finite maximal time of existence at the end of which the graphs develop a curvature singularity. We also give a rate of convergence for the singularity. © 2013 Springer-Verlag Berlin Heidelberg.

Publication Date


  • 2014

Citation


  • Wheeler, V. (2014). Non-parametric radially symmetric mean curvature flow with a free boundary. Mathematische Zeitschrift, 276 (1-2), 281-298.

Scopus Eid


  • 2-s2.0-84892490236

Ro Full-text Url


  • http://ro.uow.edu.au/cgi/viewcontent.cgi?article=3157&context=eispapers

Ro Metadata Url


  • http://ro.uow.edu.au/eispapers/2148

Has Global Citation Frequency


Number Of Pages


  • 17

Start Page


  • 281

End Page


  • 298

Volume


  • 276

Issue


  • 1-2

Place Of Publication


  • Germany

Abstract


  • We study the mean curvature flow of radially symmetric graphs with prescribed contact angle on a fixed, smooth hypersurface in Euclidean space. In this paper we treat two distinct problems. The first problem has a free Neumann boundary only, while the second has two disjoint boundaries, a free Neumann boundary and a fixed Dirichlet height. We separate the two problems and prove that under certain initial conditions we have either long time existence followed by convergence to a minimal surface, or finite maximal time of existence at the end of which the graphs develop a curvature singularity. We also give a rate of convergence for the singularity. © 2013 Springer-Verlag Berlin Heidelberg.

Publication Date


  • 2014

Citation


  • Wheeler, V. (2014). Non-parametric radially symmetric mean curvature flow with a free boundary. Mathematische Zeitschrift, 276 (1-2), 281-298.

Scopus Eid


  • 2-s2.0-84892490236

Ro Full-text Url


  • http://ro.uow.edu.au/cgi/viewcontent.cgi?article=3157&context=eispapers

Ro Metadata Url


  • http://ro.uow.edu.au/eispapers/2148

Has Global Citation Frequency


Number Of Pages


  • 17

Start Page


  • 281

End Page


  • 298

Volume


  • 276

Issue


  • 1-2

Place Of Publication


  • Germany