Center manifold: A case study

Camillo De Lellis; Emanuele Spadaro

doi:10.3934/dcds.2011.31.1249

Article Contents

2011, Volume 31, Issue 4: 1249-1272. Doi: 10.3934/dcds.2011.31.1249

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Center manifold: A case study

Camillo De Lellis^1, and
Emanuele Spadaro^2,

1.
Universität Zürich, Institut für Mathematik, Winterthurerstrasse 190, CH–8057 Zürich
2.
Hausdorff Center for Mathematics, Universität Bonn, Endenicher Allee 60, D-53115 Bonn

Received: January 31, 2010

Revised: December 31, 2010

Published: September 2011

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Abstract

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.

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Mathematics Subject Classification: Primary: 49Q15, 49Q05; Secondary: 35D10.

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References

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