# Q-valued functions revisited

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American Mathematical Society , Providence, R.I
Dirichlet principle, Geometric measure theory, Metric spaces, Harmonic
Classifications The Physical Object Statement Camillo De Lellis, Emanuele Nunzio Spadaro Series Memoirs of the American Mathematical Society -- no. 991, Memoirs of the American Mathematical Society -- no. 991. Contributions Spadaro, Emanuele Nunzio, 1983- LC Classifications QA315 .D45 2010, QA3 .A57 no.991 Pagination v, 79 p. ; Open Library OL24906061M ISBN 13 9780821849149 LC Control Number 2011002500 OCLC/WorldCa 701619878

: Q-Valued Functions Revisited (Memoirs of the American Mathematical Society) (): De Lellis, Camillo, Spadaro, Emanuele Nunzio: BooksCited by: give shorter versions of Almgren's proofs of the existence of $$\mathrm{Dir}$$-minimizing $$Q$$-valued functions, of their Hölder regularity, and of the dimension estimate of their singular set; propose an alternative, intrinsic approach to these results, not relying on Almgren's biLipschitz embedding $$\xi: \mathcal{A}_Q(\mathbb{R}^{n})\to\mathbb{R}^{N(Q,n)}$$.

- A theorem on frequency function for multiple-valued Dirichlet minimizing functions, Preprint arXiv:math/ (). William P. Ziemer, Weakly differentiable functions, Graduate Texts in Mathematics, vol.Springer-Verlag, New York, Sobolev spaces and functions of. 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 Q-valued functions revisited book versions of Almgren's proofs of the existence of. 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.

Title: Q-valued functions revisited. Authors: Camillo De Lellis, Emanuele Nunzio Spadaro (Submitted on 3 Marlast revised 17 Mar (this version, v4)) Abstract: 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 Cited by: 7. Almgren's Q-Valued Functions Revisited Article (PDF Available)   August   with  69 Reads  How we measure 'reads' A 'read' is counted each time someone views a publication summary (such as the.

Abstract: 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.

Hence, we can formulate a Dirichlet problem for Q-valued functions: f ∈W1,2(Ω,A Q)issaidtobeDir-minimizingif Dir(f,Ω)≤Dir(g,Ω) forallg∈W1,2(Ω,A Q)withf| ∂Ω =g| ∂Ω. The main results proved in this paper. We are Q-valued functions revisited book ready to state the main theorems of Almgren reproved in this note: an existence theorem and two regularityresults.

Characterization of2-d tangent Q-valued functions 67 Uniqueness of2-d tangent functions 69 Thesingularities of2-d Dir-minimizingfunctions areisolated 73 Bibliography 77 iii.

Title: Q-valued functions revisited Subject: Providence, RI, American Math. Soc., Keywords: Signatur des Originals (Print): RN 38(). Digitalisiert von der. Almgren’s Q-Valued Functions Revisited CamilloDeLellis∗ Abstract In a pioneering work written 30 years ago, Almgren developed a far-reaching reg-ularity theory for area-minimizing currents in codimension higher than 1.

Build-ing upon Almgren’s work, Chang proved later the optimal regularity statement for 2-dimensional currents. In some recent papers the author, in collaboration with Emanuele Spadaro, has simplified and extended some results of Almgren's theory, most notably the ones concerning Dir-minimizing multiple valued functions and the approximation of area-minimizing currents with small cylindrical excess.

ISBN: X: OCLC Number: Notes: "Volumenumber (first of 5 numbers)." Description: v, 79 pages ; 26 cm. Contents. CiteSeerX - Document Details (Isaac Councill, Lee Giles, Pradeep Teregowda): In this note we revisit Almgren’s theory of Q-valued functions, that are functions taking values in the space AQ(R n) of unordered Q-tuples of points in R n.

In particular: • we give shorter versions of Almgren’s proofs of the existence of Dir-minimizing Q-valued functions, of their Hölder regularity and of the. Q-valued functions revisited By Camillo De Lellis and Emanuele Nunzio Spadaro Download PDF ( KB)Author: Camillo De Lellis and Emanuele Nunzio Spadaro.

CiteSeerX - Document Details (Isaac Councill, Lee Giles, Pradeep Teregowda): In this note we revisit Almgren’s theory of Q-valued functions, that are functions taking values in the space AQ(R n) of unordered Q-tuples of points in R n.

In particular: • we give shorter versions of Almgren’s proofs of the existence of Dir-minimizing Qvalued functions, of their Hölder regularity and of the. The elementary theory of Q-valued functions --Almgren's extrinsic theory --Regularity theory --Intrinsic theory --The improved estimate of the singular set in 2 dimensions.

Series Title: Memoirs of the American Mathematical Society, no. Download PDF: Sorry, we are unable to provide the full text but you may find it at the following location(s): (external link); http://www Author: Camillo De Lellis and Emanuele Nunzio Spadaro.

De Lellis, C ().Almgren's Q-valued functions revisited. In: Proceedings of the International Congress of Mathematicians Hyderabad, India, 19 August - 27 AugustCited by: Q-valued functions.

Let Σ = Σm be an m-dimensional C1 submanifold of Rd. In what follows, integrals on Σ will always be computed with respect to the m-dimensional HausdorﬀmeasureHm deﬁnedintheambientspace. A Q-valued function onΣ isanymap u: Σ →A Q(Rn). IfB⊂Σ isameasurablesubset,everymeasurablefunctionu: B→A Q(Rn).

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_____, Q-valued functions minimizing Dirichlet’s integral and the regularity of area minimizing rectifiable currents up to codimension two., Bulletin Cited by: 3. Q-valued Functions Minimizing Dirichlet's Integral and the Regularity of Area-minimizing Rectifable Currents up to Codimension 2, Volume 1 of World Scientific Monograph Series in Mathematics.

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Find all the books, read about the author, and more. Cited by: C. D E L ELLIS, Almgren’s Q-valued functions revisited, In: “Proceedings of the International Congress of Mathematicians”, Volume III, Hindustan Book Agency, New Delhi,– Google ScholarCited by: 3. Camillo De Lellis (born J ) is an Italian mathematician who is active in the fields of calculus of variations, hyperbolic systems of conservation laws, geometric measure theory and fluid is a permanent faculty member in the School of Mathematics at the Institute for Advanced Study.

He is also one of the two managing editors of Inventiones MathematicaeAlma mater: Scuola Normale Superiore. 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.

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Here we perform a blow-up analysis deducing the regularity of area minimizing currents from that of Dir-minimizing multiple valued by:   Accepted Paper Inserted: 27 apr Last Updated: 5 apr Journal: Comm. Anal. Geom.

Year: Abstract. This is the second paper of a series of three on the regularity of higher codimension area minimizing integral currents.

Here we perform the second main step in the analysis of the singularities, namely, the construction of a center manifold, i.e., an approximate average of the sheets of an almost flat area minimizing a center manifold is accompanied by a Lipschitz Cited by:.

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