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$Q$-Valued Functions Revisited
| eBook ISBN: | 978-1-4704-0608-0 |
| Product Code: | MEMO/211/991.E |
| List Price: | $70.00 |
| MAA Member Price: | $63.00 |
| AMS Member Price: | $42.00 |
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$Q$-Valued Functions Revisited
| eBook ISBN: | 978-1-4704-0608-0 |
| Product Code: | MEMO/211/991.E |
| List Price: | $70.00 |
| MAA Member Price: | $63.00 |
| AMS Member Price: | $42.00 |
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Book DetailsMemoirs of the American Mathematical SocietyVolume: 211; 2011; 79 ppMSC: Primary 49; 35; 54; 53
In this memoir the authors revisit Almgren's theory of \(Q\)-valued functions, which are functions taking values in the space \(\mathcal{A}_Q(\mathbb{R}^{n})\) of unordered \(Q\)-tuples of points in \(\mathbb{R}^{n}\).
In particular, the authors:
- 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 \(\xi: \mathcal{A}_Q(\mathbb{R}^{n})\to\mathbb{R}^{N(Q,n)}\);
- improve upon the estimate of the singular set of planar \(\mathrm{D}\)-minimizing functions by showing that it consists of isolated points.
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Table of Contents
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Chapters
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Introduction
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1. The elementary theory of $Q$-valued functions
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2. Almgren’s extrinsic theory
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3. Regularity theory
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4. Intrinsic theory
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5. The improved estimate of the singular set in $2$ dimensions
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Volume: 211; 2011; 79 pp
MSC: Primary 49; 35; 54; 53
In this memoir the authors revisit Almgren's theory of \(Q\)-valued functions, which are functions taking values in the space \(\mathcal{A}_Q(\mathbb{R}^{n})\) of unordered \(Q\)-tuples of points in \(\mathbb{R}^{n}\).
In particular, the authors:
- 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 \(\xi: \mathcal{A}_Q(\mathbb{R}^{n})\to\mathbb{R}^{N(Q,n)}\);
- improve upon the estimate of the singular set of planar \(\mathrm{D}\)-minimizing functions by showing that it consists of isolated points.
-
Chapters
-
Introduction
-
1. The elementary theory of $Q$-valued functions
-
2. Almgren’s extrinsic theory
-
3. Regularity theory
-
4. Intrinsic theory
-
5. The improved estimate of the singular set in $2$ dimensions
Review Copy – for publishers of book reviews
Permission – for use of book, eBook, or Journal content
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