Q-valued functions revisited
By Camillo De Lellis, Emanuele Spadaro. 2008
143 citations recorded by the source corpus.
In this note we revisit Almgren's theory of Q-valued functions, that are functions taking values in the space of unordered Q-tuples of points in R^n. In particular: 1) we give shorter versions of Almgren's proofs of the existence of Dir-minimizing Q-valued functions, of their Hoelder regularity and of the dimension estimate of their singular set; 2) we propose an alternative intrinsic approach to these results, not relying on Almgren's biLipschitz embedding; 3) we improve upon the estimate of the singular set of planar Dir-minimizing functions by showing that it consists of isolated points.
Subfields: Applied Mathematics, Computer Graphics and Computer-Aided Design
View Paper: https://www.semanticscholar.org/paper/cc6956475f54a540804c56c7a868c48f48d92dbd
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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 Computer Graphics and Computer-Aided Design
Citations in the corpus
- Regularity of area minimizing currents I: gradient Lp estimates (2013, unknown): “The conclusion (iii) above is actually not explicitly stated in [13], but it follows easily: indeed”
- Multiple valued functions and integral currents (2013, methodology): “When k = 1, we denote by ∇f the vector field tangent to Σ such that 〈∇f,X〉 = DXf for every tangent vector field X .”
- Regularity of area minimizing currents II: center manifold (2013, methodology): “Since M is a graph over πH of a function ϕ̂ with ‖Dϕ̂‖C2+κ ≤ Cm 1/2 0 and since the Lipschitz constant of η ◦ f is controlled by Cmγ10 , provided ε2 is smaller than a geometric constant we have that Ω := p ( Gr(η ◦ f) C2s̄`(L)(x, πH) ) contains a ball Bs̄`(L)(p(p)).”