\`x^2+y_1+z_12^34\`
Advanced Search
Article Contents
Article Contents

Center manifold: A case study

Abstract Related Papers Cited by
  • Following Almgren's construction of the center manifold in his Big regularity paper, we show the $C^{3,\alpha}$ regularity of area-minimizing currents in the neighborhood of points of density one without using the nonparametric theory. This study is intended as a first step towards the understanding of Almgren's construction in its full generality.
    Mathematics Subject Classification: Primary: 49Q15, 49Q05; Secondary: 35D10.

    Citation:

    \begin{equation} \\ \end{equation}
  • [1]

    Frederick J. Almgren, Jr., "Almgren's Big Regularity Paper. $Q$-Valued Functions Minimizing Dirichlet's Integral and the Regularity of Area-Minimizing Rectifiable Currents up to Codimension 2," World Scientific Monograph Series in Mathematics, 1, World Scientific Publishing Co., Inc., River Edge, NJ, 2000.

    [2]

    Ennio De Giorgi, "Frontiere Orientate di Misura Minima," Seminario di Matematica della Scuola Normale Superiore di Pisa 1960-61, Editrice Tecnico Scientifica, Pisa, (1961), 57 pp.

    [3]

    Camillo De Lellis and Emanuele Nunzio SpadaroHigher integrability and approximation of minimal currents, preprint, arXiv:0910.5878v2.

    [4]

    Lawrence C. Evans and Ronald F. Gariepy, "Measure Theory and Fine Properties of Functions," Studies in Advanced Mathematics, CRC Press, Boca Raton, FL, 1992.

    [5]

    Eberhard Hopf, Über den funktionalen, insbesondere den analytischen Charakter der Lösun-gen elliptischer Differentialgleichungen zweiter Ordnung, Math. Z., 34 (1932), 194-233.doi: 10.1007/BF01180586.

    [6]

    Leon Simon, "Lectures on Geometric Measure Theory," Proceedings of the Centre for Mathematical Analysis, Australian National University, 3, Australian National University Centre for Mathematical Analysis, Canberra, 1983.

    [7]

    Elias M. Stein, "Harmonic Analysis: Real-Variable Methods, Orthogonality, and Oscillatory Integrals," Princeton Mathematical Series, 43, Monographs in Harmonic Analysis, III, Princeton University Press, Princeton, NJ, 1993.

  • 加载中
SHARE

Article Metrics

HTML views() PDF downloads(99) Cited by(0)

Access History

Other Articles By Authors

Catalog

    /

    DownLoad:  Full-Size Img  PowerPoint
    Return
    Return