This is the second paper of a series of three on the regularity of higher codimension area minimizing integral currents. Here we perform the second main step in the analysis of the singularities, namely, the construction of a center manifold, i.e., an approximate average of the sheets of an almost flat area minimizing current. Such a center manifold is accompanied by a Lipschitz multivalued map on its normal bundle, which approximates the current with a high degree of accuracy. In the third and final paper these objects are used to conclude the proof of Almgren’s celebrated dimension bound on the singular set.
Camillo De Lellis 1 ; Emanuele Spadaro 2
@article{10_4007_annals_2016_183_2_2,
author = {Camillo De Lellis and Emanuele Spadaro},
title = {Regularity of area minimizing currents {II:} center manifold},
journal = {Annals of mathematics},
pages = {499--575},
year = {2016},
volume = {183},
number = {2},
doi = {10.4007/annals.2016.183.2.2},
mrnumber = {3450482},
zbl = {06575343},
language = {en},
url = {http://geodesic.mathdoc.fr/articles/10.4007/annals.2016.183.2.2/}
}
TY - JOUR AU - Camillo De Lellis AU - Emanuele Spadaro TI - Regularity of area minimizing currents II: center manifold JO - Annals of mathematics PY - 2016 SP - 499 EP - 575 VL - 183 IS - 2 UR - http://geodesic.mathdoc.fr/articles/10.4007/annals.2016.183.2.2/ DO - 10.4007/annals.2016.183.2.2 LA - en ID - 10_4007_annals_2016_183_2_2 ER -
%0 Journal Article %A Camillo De Lellis %A Emanuele Spadaro %T Regularity of area minimizing currents II: center manifold %J Annals of mathematics %D 2016 %P 499-575 %V 183 %N 2 %U http://geodesic.mathdoc.fr/articles/10.4007/annals.2016.183.2.2/ %R 10.4007/annals.2016.183.2.2 %G en %F 10_4007_annals_2016_183_2_2
Camillo De Lellis; Emanuele Spadaro. Regularity of area minimizing currents II: center manifold. Annals of mathematics, Tome 183 (2016) no. 2, pp. 499-575. doi: 10.4007/annals.2016.183.2.2
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