N Harmonic Mappings Between Annuli

N Harmonic Mappings Between Annuli Book in PDF, ePub and Kindle version is available to download in english. Read online anytime anywhere directly from your device. Click on the download button below to get a free pdf file of N Harmonic Mappings Between Annuli book. This book definitely worth reading, it is an incredibly well-written.

N-harmonic Mappings Between Annuli

Tadeusz Iwaniec,Jani Onninen
N harmonic Mappings Between Annuli Book PDF

Author : Tadeusz Iwaniec,Jani Onninen
Publisher : American Mathematical Soc.
Page : 105 pages
File Size : 44,6 Mb
Release : 2012
Category : Mathematics
ISBN : 9780821853573

Get Book

N-harmonic Mappings Between Annuli by Tadeusz Iwaniec,Jani Onninen Pdf

The central theme of this paper is the variational analysis of homeomorphisms $h: {\mathbb X} \overset{\textnormal{\tiny{onto}}}{\longrightarrow} {\mathbb Y}$ between two given domains ${\mathbb X}, {\mathbb Y} \subset {\mathbb R}^n$. The authors look for the extremal mappings in the Sobolev space ${\mathscr W}^{1,n}({\mathbb X},{\mathbb Y})$ which minimize the energy integral ${\mathscr E}_h=\int_{{\mathbb X}} \,|\!|\, Dh(x) \,|\!|\,^n\, \textrm{d}x$. Because of the natural connections with quasiconformal mappings this $n$-harmonic alternative to the classical Dirichlet integral (for planar domains) has drawn the attention of researchers in Geometric Function Theory. Explicit analysis is made here for a pair of concentric spherical annuli where many unexpected phenomena about minimal $n$-harmonic mappings are observed. The underlying integration of nonlinear differential forms, called free Lagrangians, becomes truly a work of art.

An Introduction to the Theory of Higher-Dimensional Quasiconformal Mappings

Frederick W. Gehring,Gaven J. Martin,Bruce P. Palka
An Introduction to the Theory of Higher Dimensional Quasiconformal Mappings Book PDF

Author : Frederick W. Gehring,Gaven J. Martin,Bruce P. Palka
Publisher : American Mathematical Soc.
Page : 116 pages
File Size : 47,5 Mb
Release : 2017-05-03
Category : Conformal mapping
ISBN : 9780821843604

Get Book

An Introduction to the Theory of Higher-Dimensional Quasiconformal Mappings by Frederick W. Gehring,Gaven J. Martin,Bruce P. Palka Pdf

This book offers a modern, up-to-date introduction to quasiconformal mappings from an explicitly geometric perspective, emphasizing both the extensive developments in mapping theory during the past few decades and the remarkable applications of geometric function theory to other fields, including dynamical systems, Kleinian groups, geometric topology, differential geometry, and geometric group theory. It is a careful and detailed introduction to the higher-dimensional theory of quasiconformal mappings from the geometric viewpoint, based primarily on the technique of the conformal modulus of a curve family. Notably, the final chapter describes the application of quasiconformal mapping theory to Mostow's celebrated rigidity theorem in its original context with all the necessary background. This book will be suitable as a textbook for graduate students and researchers interested in beginning to work on mapping theory problems or learning the basics of the geometric approach to quasiconformal mappings. Only a basic background in multidimensional real analysis is assumed.

Complex Analysis and Dynamical Systems III

Mark Lʹvovich Agranovskiĭ
Complex Analysis and Dynamical Systems III Book PDF

Author : Mark Lʹvovich Agranovskiĭ
Publisher : American Mathematical Soc.
Page : 482 pages
File Size : 49,5 Mb
Release : 2008
Category : Mathematics
ISBN : 9780821841501

Get Book

Complex Analysis and Dynamical Systems III by Mark Lʹvovich Agranovskiĭ Pdf

The papers in this volume cover a wide variety of topics in the geometric theory of functions of one and several complex variables, including univalent functions, conformal and quasiconformal mappings, minimal surfaces, and dynamics in infinite-dimensional spaces. In addition, there are several articles dealing with various aspects of approximation theory and partial differential equations. Taken together, the articles collected here provide the reader with a panorama of activity in complex analysis, drawn by a number of leading figures in the field.

Modular Branching Rules for Projective Representations of Symmetric Groups and Lowering Operators for the Supergroup $Q(n)$

Aleksandr Sergeevich Kleshchëv,Vladimir Shchigolev
Modular Branching Rules for Projective Representations of Symmetric Groups and Lowering Operators for the Supergroup Q n Book PDF

Author : Aleksandr Sergeevich Kleshchëv,Vladimir Shchigolev
Publisher : American Mathematical Soc.
Page : 123 pages
File Size : 41,7 Mb
Release : 2012
Category : Mathematics
ISBN : 9780821874318

Get Book

Modular Branching Rules for Projective Representations of Symmetric Groups and Lowering Operators for the Supergroup $Q(n)$ by Aleksandr Sergeevich Kleshchëv,Vladimir Shchigolev Pdf

There are two approaches to projective representation theory of symmetric and alternating groups, which are powerful enough to work for modular representations. One is based on Sergeev duality, which connects projective representation theory of the symmetric group and representation theory of the algebraic supergroup $Q(n)$ via appropriate Schur (super)algebras and Schur functors. The second approach follows the work of Grojnowski for classical affine and cyclotomic Hecke algebras and connects projective representation theory of symmetric groups in characteristic $p$ to the crystal graph of the basic module of the twisted affine Kac-Moody algebra of type $A_{p-1}^{(2)}$. The goal of this work is to connect the two approaches mentioned above and to obtain new branching results for projective representations of symmetric groups.

The Kohn-Sham Equation for Deformed Crystals

Weinan E,Jianfeng Lu
The Kohn Sham Equation for Deformed Crystals Book PDF

Author : Weinan E,Jianfeng Lu
Publisher : American Mathematical Soc.
Page : 97 pages
File Size : 45,5 Mb
Release : 2013-01-25
Category : Mathematics
ISBN : 9780821875605

Get Book

The Kohn-Sham Equation for Deformed Crystals by Weinan E,Jianfeng Lu Pdf

The solution to the Kohn-Sham equation in the density functional theory of the quantum many-body problem is studied in the context of the electronic structure of smoothly deformed macroscopic crystals. An analog of the classical Cauchy-Born rule for crystal lattices is established for the electronic structure of the deformed crystal under the following physical conditions: (1) the band structure of the undeformed crystal has a gap, i.e. the crystal is an insulator, (2) the charge density waves are stable, and (3) the macroscopic dielectric tensor is positive definite. The effective equation governing the piezoelectric effect of a material is rigorously derived. Along the way, the authors also establish a number of fundamental properties of the Kohn-Sham map.

The Reflective Lorentzian Lattices of Rank 3

Daniel Allcock
The Reflective Lorentzian Lattices of Rank 3 Book PDF

Author : Daniel Allcock
Publisher : American Mathematical Soc.
Page : 108 pages
File Size : 42,5 Mb
Release : 2012-10-31
Category : Mathematics
ISBN : 9780821869116

Get Book

The Reflective Lorentzian Lattices of Rank 3 by Daniel Allcock Pdf

"November 2012, volume 220, Number 1033 (first of 4 numbers)."

Pseudo-Differential Operators with Discontinuous Symbols: Widom's Conjecture

Aleksandr Vladimirovich Sobolev
Pseudo Differential Operators with Discontinuous Symbols Widom s Conjecture Book PDF

Author : Aleksandr Vladimirovich Sobolev
Publisher : American Mathematical Soc.
Page : 104 pages
File Size : 52,6 Mb
Release : 2013-02-26
Category : Mathematics
ISBN : 9780821884874

Get Book

Pseudo-Differential Operators with Discontinuous Symbols: Widom's Conjecture by Aleksandr Vladimirovich Sobolev Pdf

Relying on the known two-term quasiclassical asymptotic formula for the trace of the function $f(A)$ of a Wiener-Hopf type operator $A$ in dimension one, in 1982 H. Widom conjectured a multi-dimensional generalization of that formula for a pseudo-differential operator $A$ with a symbol $a(\mathbf{x}, \boldsymbol{\xi})$ having jump discontinuities in both variables. In 1990 he proved the conjecture for the special case when the jump in any of the two variables occurs on a hyperplane. The present paper provides a proof of Widom's Conjecture under the assumption that the symbol has jumps in both variables on arbitrary smooth bounded surfaces.

Potential Wadge Classes

Dominique Lecomte
Potential Wadge Classes Book PDF

Author : Dominique Lecomte
Publisher : American Mathematical Soc.
Page : 83 pages
File Size : 50,9 Mb
Release : 2013-01-25
Category : Mathematics
ISBN : 9780821875575

Get Book

Potential Wadge Classes by Dominique Lecomte Pdf

Let $\bf\Gamma$ be a Borel class, or a Wadge class of Borel sets, and $2\!\leq\! d\!\leq\!\omega$ be a cardinal. A Borel subset $B$ of ${\mathbb R}^d$ is potentially in $\bf\Gamma$ if there is a finer Polish topology on $\mathbb R$ such that $B$ is in $\bf\Gamma$ when ${\mathbb R}^d$ is equipped with the new product topology. The author provides a way to recognize the sets potentially in $\bf\Gamma$ and applies this to the classes of graphs (oriented or not), quasi-orders and partial orders.

Characterization and Topological Rigidity of Nobeling Manifolds

Andrzej Nagórko
Characterization and Topological Rigidity of Nobeling Manifolds Book PDF

Author : Andrzej Nagórko
Publisher : American Mathematical Soc.
Page : 92 pages
File Size : 49,5 Mb
Release : 2013-04-22
Category : Mathematics
ISBN : 9780821853665

Get Book

Characterization and Topological Rigidity of Nobeling Manifolds by Andrzej Nagórko Pdf

The author develops a theory of Nobeling manifolds similar to the theory of Hilbert space manifolds. He shows that it reflects the theory of Menger manifolds developed by M. Bestvina and is its counterpart in the realm of complete spaces. In particular the author proves the Nobeling manifold characterization conjecture.

Character Identities in the Twisted Endoscopy of Real Reductive Groups

Paul Mezo
Character Identities in the Twisted Endoscopy of Real Reductive Groups Book PDF

Author : Paul Mezo
Publisher : American Mathematical Soc.
Page : 94 pages
File Size : 50,9 Mb
Release : 2013-02-26
Category : Mathematics
ISBN : 9780821875650

Get Book

Character Identities in the Twisted Endoscopy of Real Reductive Groups by Paul Mezo Pdf

Suppose $G$ is a real reductive algebraic group, $\theta$ is an automorphism of $G$, and $\omega$ is a quasicharacter of the group of real points $G(\mathbf{R})$. Under some additional assumptions, the theory of twisted endoscopy associates to this triple real reductive groups $H$. The Local Langlands Correspondence partitions the admissible representations of $H(\mathbf{R})$ and $G(\mathbf{R})$ into $L$-packets. The author proves twisted character identities between $L$-packets of $H(\mathbf{R})$ and $G(\mathbf{R})$ comprised of essential discrete series or limits of discrete series.

A Study of Singularities on Rational Curves Via Syzygies

David A. Cox,Andrew R. Kustin,Claudia Polini,Bernd Ulrich
A Study of Singularities on Rational Curves Via Syzygies Book PDF

Author : David A. Cox,Andrew R. Kustin,Claudia Polini,Bernd Ulrich
Publisher : American Mathematical Soc.
Page : 116 pages
File Size : 40,8 Mb
Release : 2013-02-26
Category : Mathematics
ISBN : 9780821887431

Get Book

A Study of Singularities on Rational Curves Via Syzygies by David A. Cox,Andrew R. Kustin,Claudia Polini,Bernd Ulrich Pdf

Consider a rational projective curve $\mathcal{C}$ of degree $d$ over an algebraically closed field $\pmb k$. There are $n$ homogeneous forms $g_{1},\dots, g_{n}$ of degree $d$ in $B=\pmb k[x, y]$ which parameterize $\mathcal{C}$ in a birational, base point free, manner. The authors study the singularities of $\mathcal{C}$ by studying a Hilbert-Burch matrix $\varphi$ for the row vector $[g_{1},\dots, g_{n}]$. In the ``General Lemma'' the authors use the generalized row ideals of $\varphi$ to identify the singular points on $\mathcal{C}$, their multiplicities, the number of branches at each singular point, and the multiplicity of each branch. Let $p$ be a singular point on the parameterized planar curve $\mathcal{C}$ which corresponds to a generalized zero of $\varphi$. In the `'triple Lemma'' the authors give a matrix $\varphi'$ whose maximal minors parameterize the closure, in $\mathbb{P}^{2}$, of the blow-up at $p$ of $\mathcal{C}$ in a neighborhood of $p$. The authors apply the General Lemma to $\varphi'$ in order to learn about the singularities of $\mathcal{C}$ in the first neighborhood of $p$. If $\mathcal{C}$ has even degree $d=2c$ and the multiplicity of $\mathcal{C}$ at $p$ is equal to $c$, then he applies the Triple Lemma again to learn about the singularities of $\mathcal{C}$ in the second neighborhood of $p$. Consider rational plane curves $\mathcal{C}$ of even degree $d=2c$. The authors classify curves according to the configuration of multiplicity $c$ singularities on or infinitely near $\mathcal{C}$. There are $7$ possible configurations of such singularities. They classify the Hilbert-Burch matrix which corresponds to each configuration. The study of multiplicity $c$ singularities on, or infinitely near, a fixed rational plane curve $\mathcal{C}$ of degree $2c$ is equivalent to the study of the scheme of generalized zeros of the fixed balanced Hilbert-Burch matrix $\varphi$ for a parameterization of $\mathcal{C}$.

The Poset of $k$-Shapes and Branching Rules for $k$-Schur Functions

Thomas Lam,Luc Lapointe,Jennifer Morse,Mark Shimozono
The Poset of k Shapes and Branching Rules for k Schur Functions Book PDF

Author : Thomas Lam,Luc Lapointe,Jennifer Morse,Mark Shimozono
Publisher : American Mathematical Soc.
Page : 101 pages
File Size : 55,9 Mb
Release : 2013-04-22
Category : Mathematics
ISBN : 9780821872949

Get Book

The Poset of $k$-Shapes and Branching Rules for $k$-Schur Functions by Thomas Lam,Luc Lapointe,Jennifer Morse,Mark Shimozono Pdf

The authors give a combinatorial expansion of a Schubert homology class in the affine Grassmannian $\mathrm{Gr}_{\mathrm{SL}_k}$ into Schubert homology classes in $\mathrm{Gr}_{\mathrm{SL}_{k+1}}$. This is achieved by studying the combinatorics of a new class of partitions called $k$-shapes, which interpolates between $k$-cores and $k+1$-cores. The authors define a symmetric function for each $k$-shape, and show that they expand positively in terms of dual $k$-Schur functions. They obtain an explicit combinatorial description of the expansion of an ungraded $k$-Schur function into $k+1$-Schur functions. As a corollary, they give a formula for the Schur expansion of an ungraded $k$-Schur function.

Connes-Chern Character for Manifolds with Boundary and Eta Cochains

Matthias Lesch,Henri Moscovici,Markus Pflaum
Connes Chern Character for Manifolds with Boundary and Eta Cochains Book PDF

Author : Matthias Lesch,Henri Moscovici,Markus Pflaum
Publisher : American Mathematical Soc.
Page : 92 pages
File Size : 55,8 Mb
Release : 2012
Category : Mathematics
ISBN : 9780821872963

Get Book

Connes-Chern Character for Manifolds with Boundary and Eta Cochains by Matthias Lesch,Henri Moscovici,Markus Pflaum Pdf

"November 2012, volume 220, number (end of volume)."

Vector Bundles on Degenerations of Elliptic Curves and Yang-Baxter Equations

Igor Burban,Bernd Kreussler
Vector Bundles on Degenerations of Elliptic Curves and Yang Baxter Equations Book PDF

Author : Igor Burban,Bernd Kreussler
Publisher : American Mathematical Soc.
Page : 131 pages
File Size : 45,9 Mb
Release : 2012
Category : Mathematics
ISBN : 9780821872925

Get Book

Vector Bundles on Degenerations of Elliptic Curves and Yang-Baxter Equations by Igor Burban,Bernd Kreussler Pdf

"November 2012, volume 220, number 1035 (third of 4 numbers)."

The Regularity of General Parabolic Systems with Degenerate Diffusion

Verena Bögelein,Frank Duzaar,Giuseppe Mingione
The Regularity of General Parabolic Systems with Degenerate Diffusion Book PDF

Author : Verena Bögelein,Frank Duzaar,Giuseppe Mingione
Publisher : American Mathematical Soc.
Page : 143 pages
File Size : 54,5 Mb
Release : 2013-01-28
Category : Mathematics
ISBN : 9780821889756

Get Book

The Regularity of General Parabolic Systems with Degenerate Diffusion by Verena Bögelein,Frank Duzaar,Giuseppe Mingione Pdf

The aim of the paper is twofold. On one hand the authors want to present a new technique called $p$-caloric approximation, which is a proper generalization of the classical compactness methods first developed by DeGiorgi with his Harmonic Approximation Lemma. This last result, initially introduced in the setting of Geometric Measure Theory to prove the regularity of minimal surfaces, is nowadays a classical tool to prove linearization and regularity results for vectorial problems. Here the authors develop a very far reaching version of this general principle devised to linearize general degenerate parabolic systems. The use of this result in turn allows the authors to achieve the subsequent and main aim of the paper, that is, the implementation of a partial regularity theory for parabolic systems with degenerate diffusion of the type $\partial_t u - \mathrm{div} a(Du)=0$, without necessarily assuming a quasi-diagonal structure, i.e. a structure prescribing that the gradient non-linearities depend only on the the explicit scalar quantity.