Quaternionic Contact Einstein Structures and the Quaternionic Contact Yamabe Problem - read free eBook in online reader or directly download on the web page. Select files or add your book in reader. Download and read online ebook Quaternionic Contact Einstein Structures and the Quaternionic Contact Yamabe Problem write by A. L. Carey. This book was released on 2014-08-12. Quaternionic Contact Einstein Structures and the Quaternionic Contact Yamabe Problem available in PDF, EPUB and Kindle. 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.
Extremals for the Sobolev Inequality and the Quaternionic Contact Yamabe Problem
Extremals for the Sobolev Inequality and the Quaternionic Contact Yamabe Problem - read free eBook in online reader or directly download on the web page. Select files or add your book in reader. Download and read online ebook Extremals for the Sobolev Inequality and the Quaternionic Contact Yamabe Problem write by Stefan P. Ivanov. This book was released on 2011. Extremals for the Sobolev Inequality and the Quaternionic Contact Yamabe Problem available in PDF, EPUB and Kindle. 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.
On the Differential Structure of Metric Measure Spaces and Applications
On the Differential Structure of Metric Measure Spaces and Applications - read free eBook in online reader or directly download on the web page. Select files or add your book in reader. Download and read online ebook On the Differential Structure of Metric Measure Spaces and Applications write by Nicola Gigli. This book was released on 2015-06-26. On the Differential Structure of Metric Measure Spaces and Applications available in PDF, EPUB and Kindle. 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.
Poincare-Einstein Holography for Forms via Conformal Geometry in the Bulk
Poincare-Einstein Holography for Forms via Conformal Geometry in the Bulk - read free eBook in online reader or directly download on the web page. Select files or add your book in reader. Download and read online ebook Poincare-Einstein Holography for Forms via Conformal Geometry in the Bulk write by A. Rod Gover. This book was released on 2015-04-09. Poincare-Einstein Holography for Forms via Conformal Geometry in the Bulk available in PDF, EPUB and Kindle. 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.
Geometric Complexity Theory IV: Nonstandard Quantum Group for the Kronecker Problem
Geometric Complexity Theory IV: Nonstandard Quantum Group for the Kronecker Problem - read free eBook in online reader or directly download on the web page. Select files or add your book in reader. Download and read online ebook Geometric Complexity Theory IV: Nonstandard Quantum Group for the Kronecker Problem write by Jonah Blasiak. This book was released on 2015-04-09. Geometric Complexity Theory IV: Nonstandard Quantum Group for the Kronecker Problem available in PDF, EPUB and Kindle. 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.
