The Ab Program In Geometric Analysis PDF Download
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Author | : Olivier Druet |
Publisher | : American Mathematical Soc. |
Total Pages | : 113 |
Release | : 2002 |
Genre | : Mathematics |
ISBN | : 0821829890 |
Download The $AB$ Program in Geometric Analysis: Sharp Sobolev Inequalities and Related Problems Book in PDF, ePub and Kindle
Function theory and Sobolev inequalities have been the target of investigation for many years. Sharp constants in these inequalities constitute a critical tool in geometric analysis. The $AB$ programme is concerned with sharp Sobolev inequalities on compact Riemannian manifolds. This text summarizes the results of contemporary research and gives an up-to-date report on the field.
Author | : Olivier Druet |
Publisher | : |
Total Pages | : 98 |
Release | : 2014-09-11 |
Genre | : Riemannian manifolds |
ISBN | : 9781470403591 |
Download The AB Program in Geometric Analysis Book in PDF, ePub and Kindle
Euclidean background Statement of the $AB$ program Some historical motivations The $H^2_1$-inequality--Part I The $H^2_1$-inequality--Part II PDE methods The isoperimetric inequality The $H^p_1$-inequalities, $1
Author | : Thierry Lévy |
Publisher | : American Mathematical Soc. |
Total Pages | : 144 |
Release | : 2003 |
Genre | : Mathematics |
ISBN | : 0821834290 |
Download Yang-Mills Measure on Compact Surfaces Book in PDF, ePub and Kindle
In this memoir we present a new construction and new properties of the Yang-Mills measure in two dimensions. This measure was first introduced for the needs of quantum field theory and can be described informally as a probability measure on the space of connections modulo gauge transformations on a principal bundle. We consider the case of a bundle over a compact orientable surface. Our construction is based on the discrete Yang-Mills theory of which we give a full acount. We are able to take its continuum limit and to define a pathwise multiplicative process of random holonomy indexed by the class of piecewise embedded loops. We study in detail the links between this process and a white noise and prove a result of asymptotic independence in the case of a semi-simple structure group. We also investigate global Markovian properties of the measure related to the surgery of surfaces.
Author | : Marcin Bownik |
Publisher | : American Mathematical Soc. |
Total Pages | : 136 |
Release | : 2003 |
Genre | : Mathematics |
ISBN | : 082183326X |
Download Anisotropic Hardy Spaces and Wavelets Book in PDF, ePub and Kindle
Investigates the anisotropic Hardy spaces associated with very general discrete groups of dilations. This book includes the classical isotropic Hardy space theory of Fefferman and Stein and parabolic Hardy space theory of Calderon and Torchinsky.
Author | : Hagen Meltzer |
Publisher | : American Mathematical Soc. |
Total Pages | : 154 |
Release | : 2004 |
Genre | : Mathematics |
ISBN | : 082183519X |
Download Exceptional Vector Bundles, Tilting Sheaves and Tilting Complexes for Weighted Projective Lines Book in PDF, ePub and Kindle
Deals with weighted projective lines, a class of non-commutative curves modelled by Geigle and Lenzing on a graded commutative sheaf theory. They play an important role in representation theory of finite-dimensional algebras; the complexity of the classification of coherent sheaves largely depends on the genus of these curves.
Author | : Ottmar Loos |
Publisher | : American Mathematical Soc. |
Total Pages | : 232 |
Release | : 2004 |
Genre | : Mathematics |
ISBN | : 0821835467 |
Download Locally Finite Root Systems Book in PDF, ePub and Kindle
We develop the basic theory of root systems $R$ in a real vector space $X$ which are defined in analogy to the usual finite root systems, except that finiteness is replaced by local finiteness: the intersection of $R$ with every finite-dimensional subspace of $X$ is finite. The main topics are Weyl groups, parabolic subsets and positive systems, weights, and gradings.
Author | : Jeff Groah |
Publisher | : American Mathematical Soc. |
Total Pages | : 98 |
Release | : 2004 |
Genre | : Mathematics |
ISBN | : 082183553X |
Download Shock-Wave Solutions of the Einstein Equations with Perfect Fluid Sources: Existence and Consistency by a Locally Inertial Glimm Scheme Book in PDF, ePub and Kindle
Demonstrates the consistency of the Einstein equations at the level of shock-waves by proving the existence of shock wave solutions of the spherically symmetric Einstein equations for a perfect fluid, starting from initial density and velocity profiles that are only locally of bounded total variation.
Author | : Masaaki Furusawa |
Publisher | : American Mathematical Soc. |
Total Pages | : 158 |
Release | : 2003 |
Genre | : Mathematics |
ISBN | : 0821833286 |
Download On Central Critical Values of the Degree Four $L$-functions for $\mathrm {GSp}(4)$: The Fundamental Lemma Book in PDF, ePub and Kindle
Proves two equalities of local Kloosterman integrals on $\mathrm{GSp}\left(4\right)$, the group of $4$ by $4$ symplectic similitude matrices. This book conjectures that both of Jacquet's relative trace formulas for the central critical values of the $L$-functions for $\mathrm{g1}\left(2\right)$ in [{J1}] and [{J2}].
Author | : Johannes Huebschmann |
Publisher | : American Mathematical Soc. |
Total Pages | : 110 |
Release | : 2004 |
Genre | : Mathematics |
ISBN | : 0821835726 |
Download Kahler Spaces, Nilpotent Orbits, and Singular Reduction Book in PDF, ePub and Kindle
For a stratified symplectic space, a suitable concept of stratified Kahler polarization encapsulates Kahler polarizations on the strata and the behaviour of the polarizations across the strata and leads to the notion of stratified Kahler space which establishes an intimate relationship between nilpotent orbits, singular reduction, invariant theory, reductive dual pairs, Jordan triple systems, symmetric domains, and pre-homogeneous spaces: The closure of a holomorphic nilpotent orbit or, equivalently, the closure of the stratum of the associated pre-homogeneous space of parabolic type carries a (positive) normal Kahler structure. In the world of singular Poisson geometry, the closures of principal holomorphic nilpotent orbits, positive definite hermitian JTS's, and certain pre-homogeneous spaces appear as different incarnations of the same structure. The closure of the principal holomorphic nilpotent orbit arises from a semisimple holomorphic orbit by contraction. Symplectic reduction carries a positive Kahler manifold to a positive normal Kahler space in such a way that the sheaf of germs of polarized functions coincides with the ordinary sheaf of germs of holomorphic functions. Symplectic reduction establishes a close relationship between singular reduced spaces and nilpotent orbits of the dual groups. Projectivization of holomorphic nilpotent orbits yields exotic (positive) stratified Kahler structures on complex projective spaces and on certain complex projective varieties including complex projective quadrics. The space of (in general twisted) representations of the fundamental group of a closed surface in a compact Lie group or, equivalently, a moduli space of central Yang-Mills connections on a principal bundle over a surface, inherits a (positive) normal (stratified) Kahler structure. Physical examples are provided by certain reduced spaces arising from angular momentum zero.
Author | : Yasuyuki Kachi |
Publisher | : American Mathematical Soc. |
Total Pages | : 133 |
Release | : 2002 |
Genre | : Mathematics |
ISBN | : 0821832255 |
Download Segre's Reflexivity and an Inductive Characterization of Hyperquadrics Book in PDF, ePub and Kindle
Introduction The universal pseudo-quotient for a family of subvarieties Normal bundles of quadrics in $X$ Morphisms from quadrics to Grassmannians Pointwise uniform vector bundles on non-singular quadrics Theory of extensions of families over Hilbert schemes Existence of algebraic quotient--proof of Theorem 0.3 Appendix. Deformations of vector bundles on infinitesimally rigid projective varieties with null global $i$-forms References