Skip to main content

Approximation problems for curvature varifolds

This is a preview of subscription content, access via your institution.


  1. [1]

    Almgren, F.J. Deformations and multiple-valued functions, inGeometric Measure Theory and the Calculus of Varia- tions, Allard, W.K. and Almgren, F.J., Eds.,Proc. Symp. Pure Math., Am. Math. Soc.,44, 29–130, (1986).

  2. [2]

    De Giorgi, E. Free Discontinuity problems in calculus of variations, inFrontiers in Pure and Applied Mathematics, a Collection of Papers Dedicated to J.L. Lions on the Occasion of his 60th Birthday, Dautray, R., Ed., North Holland, 1991.

  3. [3]

    De Giorgi, E. Introduzione ai problemi con discontinuità libere, inSymmetry in Nature: A Volume in Honour of L.A. Radicati di Brozolo, I, Scuola Normale Superiore, Pisa, 265–285, 1989.

    Google Scholar 

  4. [4]

    Delladio, S. and Scianna, G.Oriented and nonoriented curvature varifolds, Proc. Royal Soc. Edinburgh, Sect. A,125, 63–83 (1995).

    MathSciNet  MATH  Google Scholar 

  5. [5]

    Federer, H.Geometric Measure Theory, Springer, Berlin, 1969.

    MATH  Google Scholar 

  6. [6]

    Giaquinta, M., Modica, G., and Souček, J. Graphs of finite mass which cannot be approximated in area by smooth graphs,Manuscripta Mathematica,78, 259–271, (1993).

    Article  MathSciNet  MATH  Google Scholar 

  7. [7]

    Hutchinson, J.E. Second fundamental form for varifolds and the existence of surfaces minimizing curvature,Indiana Univ. Math. J.,35, 45–71, (1986).

    Article  MathSciNet  MATH  Google Scholar 

  8. [8]

    Hutchinson, J.EC 1,α multiple function regularity and tangent cone behaviour for varifolds with second fundamental form inL p, inGeometric Measure Theory and the Calculus of Variations, Allard, W.K. and Almgren, F.J., Eds.,Proc. Symp. Pure Math., Am. Math. Soc.,44, 281–306, (1986).

  9. [9]

    Hutchinson, J.E. Some regularity theory for curvature varifolds, inMiniconference on Geometry and Partial Differential Equations, Proc. Centre Math. Anal., Australian National University, Canberra,12, 60–66, (1987).

    Google Scholar 

  10. [10]

    Massey, W.S.A Basic Course in Algebraic Topology, Springer, Berlin, 1991.

    MATH  Google Scholar 

  11. [11]

    Miller, S. and Sverak, V. On surfaces with finite total curvature,J. Differential Geom.,42, 228–258 (1995).

    Google Scholar 

  12. [12]

    Rudin, W.Real and Complex Analysis, McGraw-Hill, New York, 1966.

    MATH  Google Scholar 

  13. [13]

    Simon, L. Lectures on Geometric Measure Theory,Proc. Centre for Mathematical Analysis, Australian National University,3, Canberra, 1983.

  14. [14]

    Toro, T. Functions inW 2,2(ℝ2) have Lipschitz graphs, Ph.D. Thesis, Stanford University, 1992.

Download references

Author information



Additional information

Communicated by Robert Hardt

Rights and permissions

Reprints and Permissions

About this article

Cite this article

Ambrosio, L., Gobbino, M. & Pallara, D. Approximation problems for curvature varifolds. J Geom Anal 8, 1–19 (1998).

Download citation


  • Approximation Problem
  • Fundamental Form
  • Tangent Cone
  • Sobolev Class
  • Geometric Measure Theory