Multiple valued functions and integral currents

By Camillo De Lellis, Emanuele Spadaro. 2013

68 citations recorded by the source corpus.

We prove several results on Almgren's multiple valued functions and their links to integral currents. In particular, we give a simple proof of the fact that a Lipschitz multiple valued map naturally defines an integer rectifiable current; we derive explicit formulae for the boundary, the mass and the first variations along certain specific vector-fields; and exploit this connection to derive a delicate reparametrization property for multiple valued functions. These results play a crucial role in our new proof of the partial regularity of area minimizing currents.

View Paper: https://www.semanticscholar.org/paper/6545062bb888b17948cfd89b5ee4251e90a741b5

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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.”
Regularity of area minimizing currents II: center manifold (2013, methodology): “The width of these stripes is bounded as follows: sup { |qJ(x− y)| : x, y ∈ Si } ≤ C E1/2mrJ ≤ C C 1/2m e m 1/2m 0 `(L) 1+(2−2δ2)/2m, where C is a dimensional constant.”