We provide new elementary proofs of the following two results: every complex variety is locally the graphs of a Dir-minimizing function, first proved by Almgren; the gradients of Dir-minimizing functions, in principle square-summable, are p-integrable for some p > 2, proved by De Lellis and the author. In the planar case, we prove that our integrability exponents are optimal.
Complex varieties and higher integrability of Dir-minimizing Q-valued functions / Spadaro, E. N.. - In: MANUSCRIPTA MATHEMATICA. - ISSN 0025-2611. - 132:3(2010), pp. 415-429. [10.1007/s00229-010-0353-5]
Complex varieties and higher integrability of Dir-minimizing Q-valued functions
Spadaro, E. N.
2010
Abstract
We provide new elementary proofs of the following two results: every complex variety is locally the graphs of a Dir-minimizing function, first proved by Almgren; the gradients of Dir-minimizing functions, in principle square-summable, are p-integrable for some p > 2, proved by De Lellis and the author. In the planar case, we prove that our integrability exponents are optimal.File allegati a questo prodotto
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