Regularity of area minimizing currents III: blow-up

2013

94 citations recorded by the source corpus.

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.

Subfields: Applied Mathematics, Mathematical Physics

View Paper: https://www.semanticscholar.org/paper/ef8bf05a1689facd95d80cfcae3f498b0f9dfccb

Citations in the corpus

• Multiple valued functions and integral currents (2013, unknown): “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]).”
• 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, unknown): “0.2.”