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Translating surfaces of the non-parametric mean curvature flow with prescribed contact angle

Calculus of Variations and Partial Differential Equations volume 2, pages 101–111 (1994)Cite this article

Abstract

In this work, we study surfaces over convex regions in ℝ2 which are evolving by the mean curvature flow. Here, we specify the angle of contact of the surface to the boundary cylinder. We prove that solutions converge to ones moving only by translation.

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References

  1. Altschuler, S.J.: Singularities of the curve shrinking flow for space curves. J. Diff. Geom.34, 491–514 (1991)

    Google Scholar 

  2. Altschuler, S.J., Wu, L.F.: Convergence to translating solitons for a class of quasilinear parabolic equations with fixed angle of contact to a boundary. Math. Ann.295, 761–765 (1993)

    Google Scholar 

  3. Angenent, S.B.: On the formation of singularities in the curve shortening problem. J. Diff. Geom.33, 601–633 (1991)

    Google Scholar 

  4. Gilbarg, D., Trudinger, N.S.: Elliptic partial differential equations (Grundlehren Math. Wiss., vol. 224) Berlin, Heidelberg, New York: Springer 1983

    Google Scholar 

  5. Hamilton, R.S.: Eternal solutions to the mean curvature flow. Preprint 1991

  6. Huisken, G.: Non-parametric mean curvature evolution with boundary conditions. J. Differ. Equations77, 369–378 (1989)

    Google Scholar 

  7. Huisken, G.: Asymptotic behaviour for singularities of the mean curvature flow. J. Diff. Geom.31, 285–299 (1991)

    Google Scholar 

  8. Lions, P., Trudinger, N., Urbas, J.: The Neumann problem for equations of Monge-Ampère type. Commun. Pure Appl. Math.39, 539–563 (1986)

    Google Scholar 

  9. Ladyzhenskaya, O.A., Solonnikov, V., Ural'ceva, N.: Linear and quasilinear equations of parabolic type. Transl. Math. Monogr.23A, M.S. (1968)

  10. Stone, A: The mean curvature evolution of graphs. Honour's Thesis, ANU31 (1989)

  11. Urbas, J.: Private communication 1992

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Authors and Affiliations

  1. Institute for Advanced Study, University of Princeton, 08544, Princeton, NJ, USA

    Steven J. Altschuler

  2. Mathematics Department, University of Princeton, 08544, Princeton, NJ, USA

    Lang F. Wu

Authors
  1. Steven J. Altschuler
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  2. Lang F. Wu
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Partially supported by the NSF grant no: DMS-9100383

Partially supported by the NSF grant no: DMS 9108269.A01

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Altschuler, S.J., Wu, L.F. Translating surfaces of the non-parametric mean curvature flow with prescribed contact angle. Calc. Var 2, 101–111 (1994). https://doi.org/10.1007/BF01234317

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  • DOI: https://doi.org/10.1007/BF01234317

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