Mean Curvature Flow with a Forcing Term in Minkowski Space

Research output: Contribution to journalArticleResearchpeer-review

Abstract

We study the forced mean curvature flow of graphs in Minkowski space and prove longtime existence of solutions. When the forcing term is a constant, we prove convergence to either a constant mean curvature hypersurface or a translating soliton – depending on the boundary conditions at infinity.
Original languageEnglish
Pages (from-to)205-246
Number of pages42
JournalCalculus of Variations and Partial Differential Equations
Volume25
Issue number2
Publication statusPublished - Feb 2006
Externally publishedYes

Keywords

  • Mean curvature flow
  • Constant mean curvature hypersurfaces

Cite this

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title = "Mean Curvature Flow with a Forcing Term in Minkowski Space",
abstract = "We study the forced mean curvature flow of graphs in Minkowski space and prove longtime existence of solutions. When the forcing term is a constant, we prove convergence to either a constant mean curvature hypersurface or a translating soliton – depending on the boundary conditions at infinity.",
keywords = "Mean curvature flow, Constant mean curvature hypersurfaces",
author = "Aarons, {Mark Andrew}",
year = "2006",
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journal = "Calculus of Variations and Partial Differential Equations",
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}

Mean Curvature Flow with a Forcing Term in Minkowski Space. / Aarons, Mark Andrew.

In: Calculus of Variations and Partial Differential Equations, Vol. 25, No. 2, 02.2006, p. 205-246.

Research output: Contribution to journalArticleResearchpeer-review

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AB - We study the forced mean curvature flow of graphs in Minkowski space and prove longtime existence of solutions. When the forcing term is a constant, we prove convergence to either a constant mean curvature hypersurface or a translating soliton – depending on the boundary conditions at infinity.

KW - Mean curvature flow

KW - Constant mean curvature hypersurfaces

M3 - Article

VL - 25

SP - 205

EP - 246

JO - Calculus of Variations and Partial Differential Equations

JF - Calculus of Variations and Partial Differential Equations

SN - 0944-2669

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