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A Remark on Minimal Surfaces with Corners

  • Michael Grüter
Part of the Progress in Nonlinear Differential Equations and Their Applications book series (PNLDE, volume 4)

Abstract

Here, I want to report on joint work with Leon Simon [GS].

Keywords

Free Boundary Minimal Surface Radon Measure Free Boundary Problem Tangent Cone 
These keywords were added by machine and not by the authors. This process is experimental and the keywords may be updated as the learning algorithm improves.

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References

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    W.K. Allard, On the first variation of a varifold, Ann. Math. 95 (1972), 417–491.CrossRefGoogle Scholar
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    W.K. Allard, On the first variation of a varifold: boundary behavior, Ann. Math. 101 (1975), 418–446.CrossRefGoogle Scholar
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    M. Grüter and J. Jost, Allard type regularity results for varifolds with free boundaries, Ann. Sc. Norm. Sup. Pisa (4) 13 (1986), 129–169.MATHGoogle Scholar
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    M. Grüter, The monotonicity formula in geometric measure theory, and an application to a partially free boundary problem, in: Partial Differential Equations and Calculus of Variations. Eds. S. Hildebrandt, R. Leis; Lect. Notes in Math. 1357, Springer, 1988.Google Scholar
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    M. Grüter, Regularität von minimierenden Strömen bei einer freien Randbedingung, Habilitationsschrift, Düsseldorf, 1985.Google Scholar
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    M. Grüter, Optimal regularity for codimension one minimal surfaces with a free boundary, Man. Math. 58 (1987), 295–343.Google Scholar
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    M. Grüter, Regularity results for minimizing currents with a free boundary, J. Reine Angew. Math. 375/376 (1987), 307–325.Google Scholar
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    M. Grüter and L. Simon, Regularity of minimal surfaces near corners,in preparation.Google Scholar
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    R. Hardt, and L. Simon, Boundary regularity and embedded solutions for the oriented Plateau problem, Ann. Math. 110 (1979), 439–486.MathSciNetCrossRefMATHGoogle Scholar
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    J. Jost, Continuity of minimal surfaces with piecewise smooth free boundaries, Math. Ann. 276 (1987), 599–614.MathSciNetCrossRefGoogle Scholar
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    L. Simon, Lectures on geometric measure theory, Proc. Centre for Mathematical Analysis, Australian National University, Canberra, 3, 1983.Google Scholar

Copyright information

© Springer Science+Business Media New York 1990

Authors and Affiliations

  • Michael Grüter
    • 1
  1. 1.Fachbereich MathematikUniversität des SaarlandesSaarbrückenWest Germany

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