Regularity of area minimizing currents II: center manifold
By Camillo De Lellis, Emanuele Spadaro. 2013
93 citations recorded by the source corpus.
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 center manifold is complemented with a Lipschitz multi-valued map on its normal bundle, which approximates the current with a highe degree of accuracy. In the third and final paper these objects are used to conclude a new proof of Almgren's celebrated dimension bound on the singular set.
Subfields: Applied Mathematics, Computational Theory and Mathematics
View Paper: https://www.semanticscholar.org/paper/51f35bf2e16cb474e8ad6698fe79f21748a6bd57
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In Applied Mathematics
- Emanuele Spadaro
- Camillo De Lellis
- L. Sz'ekelyhidi
- T. Buckmaster
- Vlad Vicol
- Philip Isett
- Antoine Choffrut
- Sara Daneri
In Computational Theory and Mathematics
Citations in the corpus
- Regularity of area minimizing currents I: gradient Lp estimates (2013, unknown): “Thus, unlike the two works [13, 14], which can be considered separately, the papers [15, 16, 17] are intimately interconnected.”
- Multiple valued functions and integral currents (2013, background): “In this perspective, explicit expressions for the mass and the first variations are necessary to derive the right estimates on the main geometric quantities involved in the regularity theory (cf. [5, 6, 7]).”