Supported Blow Up And Prescribed Scalar Curvature On S N
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Supported Blow Up And Prescribed Scalar Curvature On S N
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Author : Man Chun Leung
language : en
Publisher: American Mathematical Soc.
Release Date : 2011
Supported Blow Up And Prescribed Scalar Curvature On S N written by Man Chun Leung and has been published by American Mathematical Soc. this book supported file pdf, txt, epub, kindle and other format this book has been release on 2011 with Mathematics categories.
The author expounds the notion of supported blow-up and applies it to study the renowned Nirenberg/Kazdan-Warner problem on $S^n$. When $n \ge 5$ and under some mild conditions, he shows that blow-up at a point with positive definite Hessian has to be a supported isolated blow-up, which, when combined with a uniform volume bound, is a removable singularity. A new asymmetric condition is introduced to exclude single simple blow-up. These enable the author to obtain a general existence theorem for $n \ge 5$ with rather natural condition.
Supported Blow Up And Prescribed Scalar Curvature On Sn
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Author : Man Chun Leung
language : en
Publisher:
Release Date : 2011
Supported Blow Up And Prescribed Scalar Curvature On Sn written by Man Chun Leung and has been published by this book supported file pdf, txt, epub, kindle and other format this book has been release on 2011 with MATHEMATICS categories.
Vector Bundles On Degenerations Of Elliptic Curves And Yang Baxter Equations
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Author : Igor Burban
language : en
Publisher: American Mathematical Soc.
Release Date : 2012
Vector Bundles On Degenerations Of Elliptic Curves And Yang Baxter Equations written by Igor Burban and has been published by American Mathematical Soc. this book supported file pdf, txt, epub, kindle and other format this book has been release on 2012 with Mathematics categories.
"November 2012, volume 220, number 1035 (third of 4 numbers)."
On The Algebraic Foundations Of Bounded Cohomology
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Author : Theo Bühler
language : en
Publisher: American Mathematical Soc.
Release Date : 2011
On The Algebraic Foundations Of Bounded Cohomology written by Theo Bühler and has been published by American Mathematical Soc. this book supported file pdf, txt, epub, kindle and other format this book has been release on 2011 with Mathematics categories.
It is a widespread opinion among experts that (continuous) bounded cohomology cannot be interpreted as a derived functor and that triangulated methods break down. The author proves that this is wrong. He uses the formalism of exact categories and their derived categories in order to construct a classical derived functor on the category of Banach $G$-modules with values in Waelbroeck's abelian category. This gives us an axiomatic characterization of this theory for free, and it is a simple matter to reconstruct the classical semi-normed cohomology spaces out of Waelbroeck's category. The author proves that the derived categories of right bounded and of left bounded complexes of Banach $G$-modules are equivalent to the derived category of two abelian categories (one for each boundedness condition), a consequence of the theory of abstract truncation and hearts of $t$-structures. Moreover, he proves that the derived categories of Banach $G$-modules can be constructed as the homotopy categories of model structures on the categories of chain complexes of Banach $G$-modules, thus proving that the theory fits into yet another standard framework of homological and homotopical algebra.
Parabolic Systems With Polynomial Growth And Regularity
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Author : Frank Duzaar
language : en
Publisher: American Mathematical Soc.
Release Date : 2011
Parabolic Systems With Polynomial Growth And Regularity written by Frank Duzaar and has been published by American Mathematical Soc. this book supported file pdf, txt, epub, kindle and other format this book has been release on 2011 with Mathematics categories.
The authors establish a series of optimal regularity results for solutions to general non-linear parabolic systems $ u_t- \mathrm{div} \ a(x,t,u,Du)+H=0,$ under the main assumption of polynomial growth at rate $p$ i.e. $ a(x,t,u,Du) \leq L(1+ Du ^{p-1}), p \geq 2.$ They give a unified treatment of various interconnected aspects of the regularity theory: optimal partial regularity results for the spatial gradient of solutions, the first estimates on the (parabolic) Hausdorff dimension of the related singular set, and the first Calderon-Zygmund estimates for non-homogeneous problems are achieved here.
Dimer Models And Calabi Yau Algebras
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Author : Nathan Broomhead
language : en
Publisher: American Mathematical Soc.
Release Date : 2012-01-23
Dimer Models And Calabi Yau Algebras written by Nathan Broomhead and has been published by American Mathematical Soc. this book supported file pdf, txt, epub, kindle and other format this book has been release on 2012-01-23 with Mathematics categories.
In this article the author uses techniques from algebraic geometry and homological algebra, together with ideas from string theory to construct a class of 3-dimensional Calabi-Yau algebras. The Calabi-Yau property appears throughout geometry and string theory and is increasingly being studied in algebra. He further shows that the algebras constructed are examples of non-commutative crepant resolutions (NCCRs), in the sense of Van den Bergh, of Gorenstein affine toric threefolds. Dimer models, first studied in theoretical physics, give a way of writing down a class of non-commutative algebras, as the path algebra of a quiver with relations obtained from a `superpotential'. Some examples are Calabi-Yau and some are not. The author considers two types of `consistency' conditions on dimer models, and shows that a `geometrically consistent' dimer model is `algebraically consistent'. He proves that the algebras obtained from algebraically consistent dimer models are 3-dimensional Calabi-Yau algebras. This is the key step which allows him to prove that these algebras are NCCRs of the Gorenstein affine toric threefolds associated to the dimer models.
Modular Branching Rules For Projective Representations Of Symmetric Groups And Lowering Operators For The Supergroup Q N
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Author : Aleksandr Sergeevich Kleshchëv
language : en
Publisher: American Mathematical Soc.
Release Date : 2012
Modular Branching Rules For Projective Representations Of Symmetric Groups And Lowering Operators For The Supergroup Q N written by Aleksandr Sergeevich Kleshchëv and has been published by American Mathematical Soc. this book supported file pdf, txt, epub, kindle and other format this book has been release on 2012 with Mathematics categories.
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.
Supported Blow Up And Prescribed Scalar Curvature On Sn
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Author : Man Chun Leung
language : en
Publisher: American Mathematical Soc.
Release Date : 2011
Supported Blow Up And Prescribed Scalar Curvature On Sn written by Man Chun Leung and has been published by American Mathematical Soc. this book supported file pdf, txt, epub, kindle and other format this book has been release on 2011 with Mathematics categories.
"September 2011, volume 213, number 1002 (third of 5 numbers)."
General Relativistic Self Similar Waves That Induce An Anomalous Acceleration Into The Standard Model Of Cosmology
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Author : Joel Smoller
language : en
Publisher: American Mathematical Soc.
Release Date : 2012
General Relativistic Self Similar Waves That Induce An Anomalous Acceleration Into The Standard Model Of Cosmology written by Joel Smoller and has been published by American Mathematical Soc. this book supported file pdf, txt, epub, kindle and other format this book has been release on 2012 with Science categories.
The authors prove that the Einstein equations for a spherically symmetric spacetime in Standard Schwarzschild Coordinates (SSC) close to form a system of three ordinary differential equations for a family of self-similar expansion waves, and the critical ($k=0$) Friedmann universe associated with the pure radiation phase of the Standard Model of Cosmology is embedded as a single point in this family. Removing a scaling law and imposing regularity at the center, they prove that the family reduces to an implicitly defined one-parameter family of distinct spacetimes determined by the value of a new acceleration parameter $a$, such that $a=1$ corresponds to the Standard Model. The authors prove that all of the self-similar spacetimes in the family are distinct from the non-critical $k\neq0$ Friedmann spacetimes, thereby characterizing the critical $k=0$ Friedmann universe as the unique spacetime lying at the intersection of these two one-parameter families. They then present a mathematically rigorous analysis of solutions near the singular point at the center, deriving the expansion of solutions up to fourth order in the fractional distance to the Hubble Length. Finally, they use these rigorous estimates to calculate the exact leading order quadratic and cubic corrections to the redshift vs luminosity relation for an observer at the center.
A Von Neumann Algebra Approach To Quantum Metrics Quantum Relations
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Author : Greg Kuperberg
language : en
Publisher: American Mathematical Soc.
Release Date : 2012
A Von Neumann Algebra Approach To Quantum Metrics Quantum Relations written by Greg Kuperberg and has been published by American Mathematical Soc. this book supported file pdf, txt, epub, kindle and other format this book has been release on 2012 with Mathematics categories.
In A von Neumann Algebra Approach to Quantum Metrics, Kuperberg and Weaver propose a new definition of quantum metric spaces, or W*-metric spaces, in the setting of von Neumann algebras. Their definition effectively reduces to the classical notion in the atomic abelian case, has both concrete and intrinsic characterizations, and admits a wide variety of tractable examples. A natural application and motivation of their theory is a mutual generalization of the standard models of classical and quantum error correction. In Quantum Relations Weaver defines a ``quantum relation'' on a von Neumann algebra $\mathcal{M}\subseteq\mathcal{B}(H)$ to be a weak* closed operator bimodule over its commutant $\mathcal{M}'$. Although this definition is framed in terms of a particular representation of $\mathcal{M}$, it is effectively representation independent. Quantum relations on $l^\infty(X)$ exactly correspond to subsets of $X^2$, i.e., relations on $X$. There is also a good definition of a ``measurable relation'' on a measure space, to which quantum relations partially reduce in the general abelian case. By analogy with the classical setting, Weaver can identify structures such as quantum equivalence relations, quantum partial orders, and quantum graphs, and he can generalize Arveson's fundamental work on weak* closed operator algebras containing a masa to these cases. He is also able to intrinsically characterize the quantum relations on $\mathcal{M}$ in terms of families of projections in $\mathcal{M}{\overline{\otimes}} \mathcal{B}(l^2)$.