Classification Theory of Riemannian Manifolds
Title | Classification Theory of Riemannian Manifolds PDF eBook |
Author | S. R. Sario |
Publisher | |
Pages | 524 |
Release | 2014-01-15 |
Genre | |
ISBN | 9783662162927 |
Classification Theory of Riemannian Manifolds
Title | Classification Theory of Riemannian Manifolds PDF eBook |
Author | S. R. Sario |
Publisher | Springer |
Pages | 518 |
Release | 2006-11-15 |
Genre | Mathematics |
ISBN | 354037261X |
Some Results in the Classification Theory of Riemannian Manifolds
Title | Some Results in the Classification Theory of Riemannian Manifolds PDF eBook |
Author | Richard Emmanuel Katz |
Publisher | |
Pages | 94 |
Release | 1967 |
Genre | Harmonic functions |
ISBN |
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).
Leo Sario [u.a.] Classification theory of Riemannian manifolds
Title | Leo Sario [u.a.] Classification theory of Riemannian manifolds PDF eBook |
Author | Theory |
Publisher | |
Pages | |
Release | 1977 |
Genre | |
ISBN |
Lecture Notes in Mathematics
Title | Lecture Notes in Mathematics PDF eBook |
Author | |
Publisher | |
Pages | 498 |
Release | 1964 |
Genre | Harmonic functions |
ISBN | 9780387083582 |
Classification Theory of Riemann Surfaces
Title | Classification Theory of Riemann Surfaces PDF eBook |
Author | Leo Sario |
Publisher | Springer Science & Business Media |
Pages | 469 |
Release | 2012-12-06 |
Genre | Mathematics |
ISBN | 3642482694 |
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.
Classification theory of riemannian manifolds harmonic quasiharmonic and biharmonic functions
Title | Classification theory of riemannian manifolds harmonic quasiharmonic and biharmonic functions PDF eBook |
Author | L. Sario |
Publisher | |
Pages | |
Release | 1977 |
Genre | |
ISBN |