Author: Camillo De LellisPublisher:
ISBN: 9781470406080
Category : MATHEMATICS
Languages : en
Pages : 79
Book Description
Q-valued Functions Revisited
Author: Camillo De LellisPublisher:
ISBN: 9781470406080
Category : MATHEMATICS
Languages : en
Pages : 79
Book Description
Almgren's Q-valued Functions Revisited
Author: Camillo De LellisQ-valued Functions Revisited
Author: Camillo De LellisPublisher: American Mathematical Soc.
ISBN: 0821874187
Category : Mathematics
Languages : en
Pages : 92
Book Description
In this memoir the authors revisit Almgren's theory of Q-valued functions.
$Q$-Valued Functions Revisited
Author: Camillo De LellisPublisher: American Mathematical Soc.
ISBN: 082184914X
Category : Mathematics
Languages : en
Pages : 92
Book Description
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 Holder 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.
Author: Harmonic Analysis and Applications
Author: Carlos E. KenigPublisher: American Mathematical Soc.
ISBN: 1470461277
Category : Education
Languages : en
Pages : 345
Book Description
The origins of the harmonic analysis go back to an ingenious idea of Fourier that any reasonable function can be represented as an infinite linear combination of sines and cosines. Today's harmonic analysis incorporates the elements of geometric measure theory, number theory, probability, and has countless applications from data analysis to image recognition and from the study of sound and vibrations to the cutting edge of contemporary physics. The present volume is based on lectures presented at the summer school on Harmonic Analysis. These notes give fresh, concise, and high-level introductions to recent developments in the field, often with new arguments not found elsewhere. The volume will be of use both to graduate students seeking to enter the field and to senior researchers wishing to keep up with current developments.
Proceedings Of The International Congress Of Mathematicians 2010 (Icm 2010) (In 4 Volumes) - Vol. I: Plenary Lectures And Ceremonies, Vols. Ii-iv: Invited Lectures
Author: Rajendra BhatiaPublisher: World Scientific
ISBN: 9814462934
Category : Mathematics
Languages : en
Pages : 4137
Book Description
ICM 2010 proceedings comprises a four-volume set containing articles based on plenary lectures and invited section lectures, the Abel and Noether lectures, as well as contributions based on lectures delivered by the recipients of the Fields Medal, the Nevanlinna, and Chern Prizes. The first volume will also contain the speeches at the opening and closing ceremonies and other highlights of the Congress.
Q Valued Functions Minimizing Dirichlet's Integral and the Regularity of Area Minimizing Rectifiable Currents Up to Codimension Two
Author: Frederick J. AlmgrenPublisher:
ISBN:
Category : Integrals, Dirichlet
Languages : en
Pages :
Book Description
2017 MATRIX Annals
Author: Jan de GierPublisher: Springer
ISBN: 3030041611
Category : Mathematics
Languages : en
Pages : 691
Book Description
MATRIX is Australia’s international and residential mathematical research institute. It facilitates new collaborations and mathematical advances through intensive residential research programs, each 1-4 weeks in duration. This book is a scientific record of the eight programs held at MATRIX in its second year, 2017: - Hypergeometric Motives and Calabi–Yau Differential Equations - Computational Inverse Problems - Integrability in Low-Dimensional Quantum Systems - Elliptic Partial Differential Equations of Second Order: Celebrating 40 Years of Gilbarg and Trudinger’s Book - Combinatorics, Statistical Mechanics, and Conformal Field Theory - Mathematics of Risk - Tutte Centenary Retreat - Geometric R-Matrices: from Geometry to Probability The articles are grouped into peer-reviewed contributions and other contributions. The peer-reviewed articles present original results or reviews on a topic related to the MATRIX program; the remaining contributions are predominantly lecture notes or short articles based on talks or activities at MATRIX.
Almgren's Big Regularity Paper, Q-valued Functions Minimizing Dirichlet's Integral And The Regularit
Author: Vladimir SchefferPublisher: World Scientific
ISBN: 9814494119
Category : Mathematics
Languages : en
Pages : 973
Book Description
Fred Almgren exploited the excess method for proving regularity theorems in the calculus of variations. His techniques yielded Hölder continuous differentiability except for a small closed singular set. In the sixties and seventies Almgren refined and generalized his methods. Between 1974 and 1984 he wrote a 1,700-page proof that was his most ambitious development of his ground-breaking ideas. Originally, this monograph was available only as a three-volume work of limited circulation. The entire text is faithfully reproduced here.This book gives a complete proof of the interior regularity of an area-minimizing rectifiable current up to Hausdorff codimension 2. The argument uses the theory of Q-valued functions, which is developed in detail. For example, this work shows how first variation estimates from squash and squeeze deformations yield a monotonicity theorem for the normalized frequency of oscillation of a Q-valued function that minimizes a generalized Dirichlet integral. The principal features of the book include an extension theorem analogous to Kirszbraun's theorem and theorems on the approximation in mass of nearly flat mass-minimizing rectifiable currents by graphs and images of Lipschitz Q-valued functions.