Regularity of area minimizing currents III: blow-up

Camillo De Lellis; Emanuele Spadaro

doi:https://doi.org/10.4007/annals.2016.183.2.3

Abstract

This is the last of a series of three papers in which we give a new, shorter proof of a slightly improved version of Almgren’s partial regularity of area minimizing currents in Riemannian manifolds. Here we perform a blow-up analysis deducing the regularity of area minimizing currents from that of Dir-minimizing multiple valued functions.

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@article{DS1, mrkey = {2663735}, author = {De Lellis, Camillo and Spadaro, Emanuele}, title = {{$Q$}-valued functions revisited}, journal = {Mem. Amer. Math. Soc.}, fjournal = {Memoirs of the American Mathematical Society}, volume = {211}, year = {2011}, number = {991}, pages = {vi+79}, issn = {0065-9266}, coden = {MAMCAU}, isbn = {978-0-8218-4914-9}, mrclass = {49Q20 (35J50)}, mrnumber = {2663735}, mrreviewer = {Michele Miranda}, doi = {10.1090/S0065-9266-10-00607-1}, zblnumber = {1246.49001}, }
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@article{DS3, mrkey = {3283929}, author = {De Lellis, Camillo and Spadaro, Emanuele}, title = {Regularity of area minimizing currents {I}: gradient {$L\sp p$} estimates}, journal = {Geom. Funct. Anal.}, fjournal = {Geometric and Functional Analysis}, volume = {24}, year = {2014}, number = {6}, pages = {1831--1884}, issn = {1016-443X}, mrclass = {49Q15 (49N60 49Q05)}, mrnumber = {3283929}, mrreviewer = {S{\l}awomir Kolasi{ń}ski}, doi = {10.1007/s00039-014-0306-3}, zblnumber = {1307.49043}, }
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@article{DS4, author = {De Lellis, Camillo and Spadaro, Emanuele}, title = {Regularity of area-minimizing currents {II}: center manifold}, journal = {Ann. of Math.}, volume = {183}, year = {2016}, pages = {499--575}, doi={10.4007/annals.2016.183.2.2}, }
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Regularity of area minimizing currents III: blow-up

Abstract

Authors