Some Results in the Classification Theory of Riemannian 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 Some Results in the Classification Theory of Riemannian Manifolds write by Richard Emmanuel Katz. This book was released on 1967. Some Results in the Classification Theory of Riemannian Manifolds available in PDF, EPUB and Kindle. Classification theory deals with the problem of deciding which Riemann surfaces or Riemannian manifolds can carry nonconstant analytic or harmonic functions with certain restrictive properties. Depending on these properties, the author defines various 'null classes' of manifolds and considers their function-theoretic and metric characteristics as well as inclusion relations between them. (Author).
Classification Theory of Riemannian Manifolds
Classification Theory of Riemannian 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 Classification Theory of Riemannian Manifolds write by S. R. Sario. This book was released on 2014-01-15. Classification Theory of Riemannian Manifolds available in PDF, EPUB and Kindle.
Classification Theory of Riemannian Manifolds
Classification Theory of Riemannian 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 Classification Theory of Riemannian Manifolds write by S. R. Sario. This book was released on 2006-11-15. Classification Theory of Riemannian Manifolds available in PDF, EPUB and Kindle.
Classification Theory of Riemann Surfaces
Classification Theory of Riemann Surfaces - 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 Classification Theory of Riemann Surfaces write by Leo Sario. This book was released on 2012-12-06. Classification Theory of Riemann Surfaces available in PDF, EPUB and Kindle. The purpose of the present monograph is to systematically develop a classification theory of Riemann surfaces. Some first steps will also be taken toward a classification of Riemannian spaces. Four phases can be distinguished in the chronological background: the type problem; general classification; compactifications; and extension to higher dimensions. The type problem evolved in the following somewhat overlapping steps: the Riemann mapping theorem, the classical type problem, and the existence of Green's functions. The Riemann mapping theorem laid the foundation to classification theory: there are only two conformal equivalence classes of (noncompact) simply connected regions. Over half a century of efforts by leading mathematicians went into giving a rigorous proof of the theorem: RIEMANN, WEIERSTRASS, SCHWARZ, NEUMANN, POINCARE, HILBERT, WEYL, COURANT, OSGOOD, KOEBE, CARATHEODORY, MONTEL. The classical type problem was to determine whether a given simply connected covering surface of the plane is conformally equivalent to the plane or the disko The problem was in the center of interest in the thirties and early forties, with AHLFORS, KAKUTANI, KOBAYASHI, P. MYRBERG, NEVANLINNA, SPEISER, TEICHMÜLLER and others obtaining incisive specific results. The main problem of finding necessary and sufficient conditions remains, however, unsolved.
Minimal Submanifolds in Pseudo-Riemannian Geometry
Minimal Submanifolds in Pseudo-Riemannian Geometry - 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 Minimal Submanifolds in Pseudo-Riemannian Geometry write by Henri Anciaux. This book was released on 2011. Minimal Submanifolds in Pseudo-Riemannian Geometry available in PDF, EPUB and Kindle. Since the foundational work of Lagrange on the differential equation to be satisfied by a minimal surface of the Euclidean space, the theory of minimal submanifolds have undergone considerable developments, involving techniques from related areas, such as the analysis of partial differential equations and complex analysis. On the other hand, the relativity theory has led to the study of pseudo-Riemannian manifolds, which turns out to be the most general framework for the study of minimal submanifolds. However, most of the recent books on the subject still present the theory only in the Riemannian case. For the first time, this textbook provides a self-contained and accessible introduction to the subject in the general setting of pseudo-Riemannian geometry, only assuming from the reader some basic knowledge about manifold theory. Several classical results, such as the Weierstrass representation formula for minimal surfaces, and the minimizing properties of complex submanifolds, are presented in full generality without sacrificing the clarity of exposition. Finally, a number of very recent results on the subject, including the classification of equivariant minimal hypersurfaces in pseudo-Riemannian space forms and the characterization of minimal Lagrangian surfaces in some pseudo-Khler manifolds are given.
