 | De Lellis C. Q-valued functions revisited / C. De Lellis, E.N.Spadaro. - Providence: American Mathematical Society, 2011. - v, 79 p. - (Memoirs of the American Mathematical Society; vol.211, N 991). - Bibliogr.: p.77-79. - ISBN 978-0-8218-4914-9; ISSN 0065-9266
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Introduction .................................................... 1
Chapter 1. The elementary theory of Q-valued functions ......... 7
1.1 Decomposition and selection for Q-valued functions ......... 7
1.2 Extension of Lipschitz Q-valued functions ................. 11
1.3 Differentiability and Rademacher's Theorem ................ 14
Chapter 2. Almgren's extrinsic theory ......................... 19
2.1 The biLipschitz embedding ξ and the retraction ρ .......... 19
2.2 Properties of Q-valued Sobolev functions .................. 23
2.3 Existence of Dir-minimizing Q-valued functions ............ 27
Chapter 3. Regularity theory .................................. 31
3.1 First variations .......................................... 31
3.2 A maximum principle for Q-valued functions ................ 33
3.3 Holder regularity ......................................... 36
3.4 Frequency function ........................................ 42
3.5 Blow-up of Dir-minimizing Q-valued functions .............. 44
3.6 Estimate of the singular set .............................. 46
Chapter 4. Intrinsic theory ................................... 53
4.1 Metric Sobolev spaces ..................................... 53
4.2 Metric proofs of the main theorems I ...................... 55
4.3 Metric proofs of the main theorems II ..................... 59
Chapter 5. The improved estimate of the singular set
in 2 dimensions .................................... 67
5.1 Characterization of 2-d tangent Q-valued functions ........ 67
5.2 Uniqueness of 2-d tangent functions ....................... 69
5.3 The singularities of 2-d Dir-minimizing functions are
isolated .................................................. 73
Bibliography ................................................... 77
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