The Universal Kobayashi-Hitchin Correspondence on Hermitian Manifolds - 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 The Universal Kobayashi-Hitchin Correspondence on Hermitian Manifolds write by Martin Lübke. This book was released on 2006. The Universal Kobayashi-Hitchin Correspondence on Hermitian Manifolds available in PDF, EPUB and Kindle. We prove a very general Kobayashi-Hitchin correspondence on arbitrary compact Hermitian manifolds, and we discuss differential geometric properties of the corresponding moduli spaces. This correspondence refers to moduli spaces of ``universal holomorphic oriented pairs''. Most of the classical moduli problems in complex geometry (e. g. holomorphic bundles with reductive structure groups, holomorphic pairs, holomorphic Higgs pairs, Witten triples, arbitrary quiver moduli problems) are special cases of this universal classification problem. Our Kobayashi-Hitchin correspondence relates the complex geometric concept ``polystable oriented holomorphic pair'' to the existence of a reduction solving a generalized Hermitian-Einstein equation. The proof is based on the Uhlenbeck-Yau continuity method. Using ideas from Donaldson theory, we further introduce and investigate canonical Hermitian metrics on such moduli spaces. We discuss in detail remarkable classes of moduli spaces in the non-Kahlerian framework: Oriented holomorphic structures, Quot-spaces, oriented holomorphic pairs and oriented vortices, non-abelian Seiberg-Witten monopoles.
Space – Time – Matter
Space – Time – Matter - 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 Space – Time – Matter write by Jochen Brüning. This book was released on 2018-04-09. Space – Time – Matter available 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
Weil-Petersson Metric on the Universal Teichmuller Space
Weil-Petersson Metric on the Universal Teichmuller Space - 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 Weil-Petersson Metric on the Universal Teichmuller Space write by Leon Armenovich Takhtadzhi︠a︡n. This book was released on 2006. Weil-Petersson Metric on the Universal Teichmuller Space available in PDF, EPUB and Kindle. In this memoir, we prove that the universal Teichmuller space $T(1)$ carries a new structure of a complex Hilbert manifold and show that the connected component of the identity of $T(1)$ -- the Hilbert submanifold $T {0 (1)$ -- is a topological group. We define a Weil-Petersson metric on $T(1)$ by Hilbert space inner products on tangent spaces, compute its Riemann curvature tensor, and show that $T(1)$ is a Kahler-Einstein manifold with negative Ricci and sectional curvatures. We introduce and compute Mumford-Miller-Morita characteristic forms for the vertical tangent bundle of the universal Teichmuller curve fibration over the universal Teichmuller space. As an application, we derive Wolpert curvature formulas for the finite-dimensional Teichmuller spaces from the formulas for the universal Teichmuller space. We study in detail the Hilbert manifold structure on $T {0 (1)$ and characterize points on $T {0 (1)$ in terms of Bers and pre-Bers embeddings by proving that the Grunsky operators $B {1 $ and The results of this memoir were presented in our e-prints: Weil-Petersson metric on the universal Teichmuller space I. Curvature properties and Chern forms, arXiv:math.CV/0312172 (2003), and Weil-Petersson metric on the universal Teichmuller space II. Kahler potential and period mapping, arXiv:math.CV/0406408 (2004).
Weakly Differentiable Mappings between Manifolds
Weakly Differentiable Mappings between Manifolds - 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 Weakly Differentiable Mappings between Manifolds write by Piotr Hajłasz. This book was released on 2008. Weakly Differentiable Mappings between Manifolds available in PDF, EPUB and Kindle. The authors study Sobolev classes of weakly differentiable mappings $f: {\mathbb X}\rightarrow {\mathbb Y}$ between compact Riemannian manifolds without boundary. These mappings need not be continuous. They actually possess less regularity than the mappings in ${\mathcal W}{1, n}({\mathbb X}\, \, {\mathbb Y})\, $, $n=\mbox{dim}\, {\mathbb X}$. The central themes being discussed a
Fredholm Operators and Einstein Metrics on Conformally Compact Manifolds
Fredholm Operators and Einstein Metrics on Conformally Compact Manifolds - 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 Fredholm Operators and Einstein Metrics on Conformally Compact Manifolds write by John M. Lee. This book was released on 2006. Fredholm Operators and Einstein Metrics on Conformally Compact Manifolds available in PDF, EPUB and Kindle. "Volume 183, number 864 (end of volume)."
