Quaternionic Contact Einstein Structures And The Quaternionic Contact Yamabe Problem

Author : A. L. Carey,V. Gayral,A. Rennie,F. A. Sukochev
Publisher : American Mathematical Soc.
Page : 82 pages
File Size : 42,7 Mb
Release : 2014-08-12
Category : Mathematics
ISBN : 9780821898437

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Quaternionic Contact Einstein Structures and the Quaternionic Contact Yamabe Problem by A. L. Carey,V. Gayral,A. Rennie,F. A. Sukochev Pdf

A partial solution of the quaternionic contact Yamabe problem on the quaternionic sphere is given. It is shown that the torsion of the Biquard connection vanishes exactly when the trace-free part of the horizontal Ricci tensor of the Biquard connection is zero and this occurs precisely on 3-Sasakian manifolds. All conformal transformations sending the standard flat torsion-free quaternionic contact structure on the quaternionic Heisenberg group to a quaternionic contact structure with vanishing torsion of the Biquard connection are explicitly described. A "3-Hamiltonian form" of infinitesimal conformal automorphisms of quaternionic contact structures is presented.

Author : Stefan P. Ivanov,Ivan Minchev (Mathematics professor),Dimiter N. Vassilev
Publisher : Unknown
Page : 82 pages
File Size : 44,8 Mb
Release : 2014
Category : Contact manifolds
ISBN : 1470417227

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Quaternionic Contact by Stefan P. Ivanov,Ivan Minchev (Mathematics professor),Dimiter N. Vassilev Pdf

"Volume 231, number 1086 (third of 5 numbers), September 2014."

Author : Anonim
Publisher : Unknown
Page : 128 pages
File Size : 50,7 Mb
Release : 2024-07-01
Category : Electronic
ISBN : 9789814465557

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Extremals for the Sobolev Inequality and the Quaternionic Contact Yamabe Problem by Anonim Pdf

Author : Stefan P. Ivanov,Dimiter N. Vassilev
Publisher : World Scientific
Page : 238 pages
File Size : 48,5 Mb
Release : 2011
Category : Mathematics
ISBN : 9789814295703

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Extremals for the Sobolev Inequality and the Quaternionic Contact Yamabe Problem by Stefan P. Ivanov,Dimiter N. Vassilev Pdf

The aim of this book is to give an account of some important new developments in the study of the Yamabe problem on quaternionic contact manifolds. This book covers the conformally flat case of the quaternionic Heisenberg group or sphere, where complete and detailed proofs are given, together with a chapter on the conformal curvature tensor introduced very recently by the authors. The starting point of the considered problems is the well-known Folland?Stein Sobolev type embedding and its sharp form that is determined based on geometric analysis. This book also sits at the interface of the generalization of these fundamental questions motivated by the Carnot?Caratheodory geometry of quaternionic contact manifolds, which have been recently the focus of extensive research motivated by problems in analysis, geometry, mathematical physics and the applied sciences. Through the beautiful resolution of the Yamabe problem on model quaternionic contact spaces, the book serves as an introduction to this field for graduate students and novice researchers, and as a research monograph suitable for experts as well.

Author : Nicola Gigli
Publisher : American Mathematical Soc.
Page : 91 pages
File Size : 53,8 Mb
Release : 2015-06-26
Category : Differential calculus
ISBN : 9781470414207

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On the Differential Structure of Metric Measure Spaces and Applications by Nicola Gigli Pdf

The main goals of this paper are: (i) To develop an abstract differential calculus on metric measure spaces by investigating the duality relations between differentials and gradients of Sobolev functions. This will be achieved without calling into play any sort of analysis in charts, our assumptions being: the metric space is complete and separable and the measure is Radon and non-negative. (ii) To employ these notions of calculus to provide, via integration by parts, a general definition of distributional Laplacian, thus giving a meaning to an expression like , where is a function and is a measure. (iii) To show that on spaces with Ricci curvature bounded from below and dimension bounded from above, the Laplacian of the distance function is always a measure and that this measure has the standard sharp comparison properties. This result requires an additional assumption on the space, which reduces to strict convexity of the norm in the case of smooth Finsler structures and is always satisfied on spaces with linear Laplacian, a situation which is analyzed in detail.

Author : A. Rod Gover,Emanuele Latini,Andrew Waldron
Publisher : American Mathematical Soc.
Page : 85 pages
File Size : 50,7 Mb
Release : 2015-04-09
Category : Mathematics
ISBN : 9781470410926

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Poincare-Einstein Holography for Forms via Conformal Geometry in the Bulk by A. Rod Gover,Emanuele Latini,Andrew Waldron Pdf

The authors study higher form Proca equations on Einstein manifolds with boundary data along conformal infinity. They solve these Laplace-type boundary problems formally, and to all orders, by constructing an operator which projects arbitrary forms to solutions. They also develop a product formula for solving these asymptotic problems in general. The central tools of their approach are (i) the conformal geometry of differential forms and the associated exterior tractor calculus, and (ii) a generalised notion of scale which encodes the connection between the underlying geometry and its boundary. The latter also controls the breaking of conformal invariance in a very strict way by coupling conformally invariant equations to the scale tractor associated with the generalised scale.

Author : Jonah Blasiak,Ketan D. Mulmuley,Milind Sohoni
Publisher : American Mathematical Soc.
Page : 160 pages
File Size : 40,7 Mb
Release : 2015-04-09
Category : Mathematics
ISBN : 9781470410117

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Geometric Complexity Theory IV: Nonstandard Quantum Group for the Kronecker Problem by Jonah Blasiak,Ketan D. Mulmuley,Milind Sohoni Pdf

The Kronecker coefficient is the multiplicity of the -irreducible in the restriction of the -irreducible via the natural map , where are -vector spaces and . A fundamental open problem in algebraic combinatorics is to find a positive combinatorial formula for these coefficients. The authors construct two quantum objects for this problem, which they call the nonstandard quantum group and nonstandard Hecke algebra. They show that the nonstandard quantum group has a compact real form and its representations are completely reducible, that the nonstandard Hecke algebra is semisimple, and that they satisfy an analog of quantum Schur-Weyl duality.

Author : Pierre Bieliavsky,Victor Gayral
Publisher : American Mathematical Soc.
Page : 154 pages
File Size : 55,6 Mb
Release : 2015-06-26
Category : Kählerian structures
ISBN : 9781470414917

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Deformation Quantization for Actions of Kahlerian Lie Groups by Pierre Bieliavsky,Victor Gayral Pdf

Let B be a Lie group admitting a left-invariant negatively curved Kählerian structure. Consider a strongly continuous action of B on a Fréchet algebra . Denote by the associated Fréchet algebra of smooth vectors for this action. In the Abelian case BR and isometric, Marc Rieffel proved that Weyl's operator symbol composition formula (the so called Moyal product) yields a deformation through Fréchet algebra structures R on . When is a -algebra, every deformed Fréchet algebra admits a compatible pre- -structure, hence yielding a deformation theory at the level of -algebras too. In this memoir, the authors prove both analogous statements for general negatively curved Kählerian groups. The construction relies on the one hand on combining a non-Abelian version of oscillatory integral on tempered Lie groups with geom,etrical objects coming from invariant WKB-quantization of solvable symplectic symmetric spaces, and, on the second hand, in establishing a non-Abelian version of the Calderón-Vaillancourt Theorem. In particular, the authors give an oscillating kernel formula for WKB-star products on symplectic symmetric spaces that fiber over an exponential Lie group.

Author : Gaëtan Chenevier, David A. Renard
Publisher : American Mathematical Soc.
Page : 122 pages
File Size : 48,8 Mb
Release : 2015-08-21
Category : Cusp forms (Mathematics)
ISBN : 9781470410940

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Level One Algebraic Cusp Forms of Classical Groups of Small Rank by Gaëtan Chenevier, David A. Renard Pdf

The authors determine the number of level 1, polarized, algebraic regular, cuspidal automorphic representations of GLn over Q of any given infinitesimal character, for essentially all n≤8. For this, they compute the dimensions of spaces of level 1 automorphic forms for certain semisimple Z-forms of the compact groups SO7, SO8, SO9 (and G2) and determine Arthur's endoscopic partition of these spaces in all cases. They also give applications to the 121 even lattices of rank 25 and determinant 2 found by Borcherds, to level one self-dual automorphic representations of GLn with trivial infinitesimal character, and to vector valued Siegel modular forms of genus 3. A part of the authors' results are conditional to certain expected results in the theory of twisted endoscopy.

Author : Joonil Kim
Publisher : American Mathematical Soc.
Page : 120 pages
File Size : 40,7 Mb
Release : 2015-08-21
Category : Hilbert transform
ISBN : 9781470414351

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Multiple Hilbert Transforms Associated with Polynomials by Joonil Kim Pdf

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Author : Volodymyr Nekrashevych
Publisher : American Mathematical Soc.
Page : 108 pages
File Size : 45,5 Mb
Release : 2015-08-21
Category : Duality theory (Mathematics)
ISBN : 9781470415440

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Hyperbolic Groupoids and Duality by Volodymyr Nekrashevych Pdf

The author introduces a notion of hyperbolic groupoids, generalizing the notion of a Gromov hyperbolic group. Examples of hyperbolic groupoids include actions of Gromov hyperbolic groups on their boundaries, pseudogroups generated by expanding self-coverings, natural pseudogroups acting on leaves of stable (or unstable) foliation of an Anosov diffeomorphism, etc. The author describes a duality theory for hyperbolic groupoids. He shows that for every hyperbolic groupoid G there is a naturally defined dual groupoid G⊤ acting on the Gromov boundary of a Cayley graph of G. The groupoid G⊤ is also hyperbolic and such that (G⊤)⊤ is equivalent to G. Several classes of examples of hyperbolic groupoids and their applications are discussed.

Author : Paul Seidel
Publisher : American Mathematical Soc.
Page : 236 pages
File Size : 51,5 Mb
Release : 2015-06-26
Category : Mirror symmetry
ISBN : 9781470410971

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Homological Mirror Symmetry for the Quartic Surface by Paul Seidel Pdf

The author proves Kontsevich's form of the mirror symmetry conjecture for (on the symplectic geometry side) a quartic surface in C .

Author : Chih-Yun Chuang,Ting-Fang Lee, Fu-Tsun Wei,Jing Yu
Publisher : American Mathematical Soc.
Page : 64 pages
File Size : 44,6 Mb
Release : 2015-08-21
Category : Hecke algebras
ISBN : 9781470414191

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Brandt Matrices and Theta Series over Global Function Fields by Chih-Yun Chuang,Ting-Fang Lee, Fu-Tsun Wei,Jing Yu Pdf

The aim of this article is to give a complete account of the Eichler-Brandt theory over function fields and the basis problem for Drinfeld type automorphic forms. Given arbitrary function field k together with a fixed place ∞, the authors construct a family of theta series from the norm forms of "definite" quaternion algebras, and establish an explicit Hecke-module homomorphism from the Picard group of an associated definite Shimura curve to a space of Drinfeld type automorphic forms. The "compatibility" of these homomorphisms with different square-free levels is also examined. These Hecke-equivariant maps lead to a nice description of the subspace generated by the authors' theta series, and thereby contributes to the so-called basis problem. Restricting the norm forms to pure quaternions, the authors obtain another family of theta series which are automorphic functions on the metaplectic group, and this results in a Shintani-type correspondence between Drinfeld type forms and metaplectic forms.

Author : R. Bruggeman,J. Lewis,D. Zagier
Publisher : American Mathematical Soc.
Page : 132 pages
File Size : 48,7 Mb
Release : 2015-08-21
Category : Algebraic topology
ISBN : 9781470414078

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Period Functions for Maass Wave Forms and Cohomology by R. Bruggeman,J. Lewis,D. Zagier Pdf

The authors construct explicit isomorphisms between spaces of Maass wave forms and cohomology groups for discrete cofinite groups Γ⊂PSL2(R). In the case that Γ is the modular group PSL2(Z) this gives a cohomological framework for the results in Period functions for Maass wave forms. I, of J. Lewis and D. Zagier in Ann. Math. 153 (2001), 191-258, where a bijection was given between cuspidal Maass forms and period functions. The authors introduce the concepts of mixed parabolic cohomology group and semi-analytic vectors in principal series representation. This enables them to describe cohomology groups isomorphic to spaces of Maass cusp forms, spaces spanned by residues of Eisenstein series, and spaces of all Γ-invariant eigenfunctions of the Laplace operator. For spaces of Maass cusp forms the authors also describe isomorphisms to parabolic cohomology groups with smooth coefficients and standard cohomology groups with distribution coefficients. They use the latter correspondence to relate the Petersson scalar product to the cup product in cohomology.

Author : Robert C. Dalang,Marta Sanz-Solé
Publisher : American Mathematical Soc.
Page : 75 pages
File Size : 45,7 Mb
Release : 2015-08-21
Category : Hausdorff measures
ISBN : 9781470414238

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Hitting Probabilities for Nonlinear Systems of Stochastic Waves by Robert C. Dalang,Marta Sanz-Solé Pdf

The authors consider a d-dimensional random field u={u(t,x)} that solves a non-linear system of stochastic wave equations in spatial dimensions k∈{1,2,3}, driven by a spatially homogeneous Gaussian noise that is white in time. They mainly consider the case where the spatial covariance is given by a Riesz kernel with exponent β. Using Malliavin calculus, they establish upper and lower bounds on the probabilities that the random field visits a deterministic subset of Rd, in terms, respectively, of Hausdorff measure and Newtonian capacity of this set. The dimension that appears in the Hausdorff measure is close to optimal, and shows that when d(2−β)>2(k+1), points are polar for u. Conversely, in low dimensions d, points are not polar. There is, however, an interval in which the question of polarity of points remains open.