Compact Quotients Of Cahen Wallach Spaces
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Compact Quotients of Cahen Wallach Spaces
Author | : Ines Kath,Martin Olbrich |
Publsiher | : American Mathematical Soc. |
Total Pages | : 84 |
Release | : 2020-02-13 |
Genre | : Education |
ISBN | : 9781470441036 |
Download Compact Quotients of Cahen Wallach Spaces Book in PDF, Epub and Kindle
Indecomposable symmetric Lorentzian manifolds of non-constant curvature are called Cahen-Wallach spaces. Their isometry classes are described by continuous families of real parameters. The authors derive necessary and sufficient conditions for the existence of compact quotients of Cahen-Wallach spaces in terms of these parameters.
Space Time Matter
Author | : Jochen Brüning,Matthias Staudacher |
Publsiher | : Walter de Gruyter GmbH & Co KG |
Total Pages | : 517 |
Release | : 2018-04-09 |
Genre | : Mathematics |
ISBN | : 9783110452150 |
Download Space Time Matter Book in PDF, Epub and Kindle
This monograph describes some of the most interesting results obtained by the mathematicians and physicists collaborating in the CRC 647 "Space – Time – Matter", in the years 2005 - 2016. The work presented concerns the mathematical and physical foundations of string and quantum field theory as well as cosmology. Important topics are the spaces and metrics modelling the geometry of matter, and the evolution of these geometries. The partial differential equations governing such structures and their singularities, special solutions and stability properties are discussed in detail. Contents Introduction Algebraic K-theory, assembly maps, controlled algebra, and trace methods Lorentzian manifolds with special holonomy – Constructions and global properties Contributions to the spectral geometry of locally homogeneous spaces On conformally covariant differential operators and spectral theory of the holographic Laplacian Moduli and deformations Vector bundles in algebraic geometry and mathematical physics Dyson–Schwinger equations: Fix-point equations for quantum fields Hidden structure in the form factors ofN = 4 SYM On regulating the AdS superstring Constraints on CFT observables from the bootstrap program Simplifying amplitudes in Maxwell-Einstein and Yang-Mills-Einstein supergravities Yangian symmetry in maximally supersymmetric Yang-Mills theory Wave and Dirac equations on manifolds Geometric analysis on singular spaces Singularities and long-time behavior in nonlinear evolution equations and general relativity
Global Well Posedness of High Dimensional Maxwell Dirac for Small Critical Data
Author | : Cristian Gavrus,Sung-Jin Oh |
Publsiher | : American Mathematical Soc. |
Total Pages | : 94 |
Release | : 2020-05-13 |
Genre | : Education |
ISBN | : 9781470441111 |
Download Global Well Posedness of High Dimensional Maxwell Dirac for Small Critical Data Book in PDF, Epub and Kindle
In this paper, the authors prove global well-posedness of the massless Maxwell–Dirac equation in the Coulomb gauge on R1+d(d≥4) for data with small scale-critical Sobolev norm, as well as modified scattering of the solutions. Main components of the authors' proof are A) uncovering null structure of Maxwell–Dirac in the Coulomb gauge, and B) proving solvability of the underlying covariant Dirac equation. A key step for achieving both is to exploit (and justify) a deep analogy between Maxwell–Dirac and Maxwell-Klein-Gordon (for which an analogous result was proved earlier by Krieger-Sterbenz-Tataru, which says that the most difficult part of Maxwell–Dirac takes essentially the same form as Maxwell-Klein-Gordon.
Global Smooth Solutions for the Inviscid SQG Equation
Author | : Angel Castro,Diego Cordoba,Javier Gomez-Serrano |
Publsiher | : American Mathematical Soc. |
Total Pages | : 89 |
Release | : 2020-09-28 |
Genre | : Mathematics |
ISBN | : 9781470442149 |
Download Global Smooth Solutions for the Inviscid SQG Equation Book in PDF, Epub and Kindle
In this paper, the authors show the existence of the first non trivial family of classical global solutions of the inviscid surface quasi-geostrophic equation.
Dynamics Near the Subcritical Transition of the 3D Couette Flow I Below Threshold Case
Author | : Jacob Bedrossian,Pierre Germain,Nader Masmoudi |
Publsiher | : American Mathematical Soc. |
Total Pages | : 154 |
Release | : 2020-09-28 |
Genre | : Mathematics |
ISBN | : 9781470442170 |
Download Dynamics Near the Subcritical Transition of the 3D Couette Flow I Below Threshold Case Book in PDF, Epub and Kindle
The authors study small disturbances to the periodic, plane Couette flow in the 3D incompressible Navier-Stokes equations at high Reynolds number Re. They prove that for sufficiently regular initial data of size $epsilon leq c_0mathbf {Re}^-1$ for some universal $c_0 > 0$, the solution is global, remains within $O(c_0)$ of the Couette flow in $L^2$, and returns to the Couette flow as $t rightarrow infty $. For times $t gtrsim mathbf {Re}^1/3$, the streamwise dependence is damped by a mixing-enhanced dissipation effect and the solution is rapidly attracted to the class of ``2.5 dimensional'' streamwise-independent solutions referred to as streaks.
The Riesz Transform of Codimension Smaller Than One and the Wolff Energy
Author | : Benjamin Jaye,Fedor Nazarov,Maria Carmen Reguera,Xavier Tolsa |
Publsiher | : American Mathematical Soc. |
Total Pages | : 97 |
Release | : 2020-09-28 |
Genre | : Mathematics |
ISBN | : 9781470442132 |
Download The Riesz Transform of Codimension Smaller Than One and the Wolff Energy Book in PDF, Epub and Kindle
Fix $dgeq 2$, and $sin (d-1,d)$. The authors characterize the non-negative locally finite non-atomic Borel measures $mu $ in $mathbb R^d$ for which the associated $s$-Riesz transform is bounded in $L^2(mu )$ in terms of the Wolff energy. This extends the range of $s$ in which the Mateu-Prat-Verdera characterization of measures with bounded $s$-Riesz transform is known. As an application, the authors give a metric characterization of the removable sets for locally Lipschitz continuous solutions of the fractional Laplacian operator $(-Delta )^alpha /2$, $alpha in (1,2)$, in terms of a well-known capacity from non-linear potential theory. This result contrasts sharply with removability results for Lipschitz harmonic functions.
Conformal Graph Directed Markov Systems on Carnot Groups
Author | : Vasileios Chousionis,Jeremy T. Tyson,Mariusz Urbanski |
Publsiher | : American Mathematical Soc. |
Total Pages | : 153 |
Release | : 2020-09-28 |
Genre | : Mathematics |
ISBN | : 9781470442156 |
Download Conformal Graph Directed Markov Systems on Carnot Groups Book in PDF, Epub and Kindle
The authors develop a comprehensive theory of conformal graph directed Markov systems in the non-Riemannian setting of Carnot groups equipped with a sub-Riemannian metric. In particular, they develop the thermodynamic formalism and show that, under natural hypotheses, the limit set of an Carnot conformal GDMS has Hausdorff dimension given by Bowen's parameter. They illustrate their results for a variety of examples of both linear and nonlinear iterated function systems and graph directed Markov systems in such sub-Riemannian spaces. These include the Heisenberg continued fractions introduced by Lukyanenko and Vandehey as well as Kleinian and Schottky groups associated to the non-real classical rank one hyperbolic spaces.
Explicit Arithmetic of Jacobians of Generalized Legendre Curves Over Global Function Fields
Author | : Lisa Berger,Chris Hall,Rene Pannekoek,Rachel Pries,Shahed Sharif |
Publsiher | : American Mathematical Soc. |
Total Pages | : 131 |
Release | : 2020-09-28 |
Genre | : Mathematics |
ISBN | : 9781470442194 |
Download Explicit Arithmetic of Jacobians of Generalized Legendre Curves Over Global Function Fields Book in PDF, Epub and Kindle
The authors study the Jacobian $J$ of the smooth projective curve $C$ of genus $r-1$ with affine model $y^r = x^r-1(x + 1)(x + t)$ over the function field $mathbb F_p(t)$, when $p$ is prime and $rge 2$ is an integer prime to $p$. When $q$ is a power of $p$ and $d$ is a positive integer, the authors compute the $L$-function of $J$ over $mathbb F_q(t^1/d)$ and show that the Birch and Swinnerton-Dyer conjecture holds for $J$ over $mathbb F_q(t^1/d)$.