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This book proves an analogue of William Thurston's celebrated hyperbolic Dehn surgery theorem in the context of complex hyperbolic discrete groups, and then derives two main geometric consequences from it. The first is the construction of large numbers of closed real hyperbolic 3-manifolds which bound complex hyperbolic orbifolds--the only known examples of closed manifolds that simultaneously have these two kinds of geometric structures. The second is a complete understanding of the structure of complex hyperbolic reflection triangle groups in cases where the angle is small. In an accessible and straightforward manner, Richard Evan Schwartz also presents a large amount of useful information on complex hyperbolic geometry and discrete groups. Schwartz relies on elementary proofs and avoids "ations of preexisting technical material as much as possible. For this reason, this book will benefit graduate students seeking entry into this emerging area of research, as well as researchers in allied fields such as Kleinian groups and CR geometry.

CR submanifolds. --- Dehn surgery (Topology). --- Three-manifolds (Topology). --- CR submanifolds --- Dehn surgery (Topology) --- Three-manifolds (Topology) --- Mathematics --- Physical Sciences & Mathematics --- Geometry --- 3-manifolds (Topology) --- Manifolds, Three dimensional (Topology) --- Three-dimensional manifolds (Topology) --- Cauchy-Riemann submanifolds --- Submanifolds, CR --- Low-dimensional topology --- Topological manifolds --- Surgery (Topology) --- Manifolds (Mathematics) --- Arc (geometry). --- Automorphism. --- Ball (mathematics). --- Bijection. --- Bump function. --- CR manifold. --- Calculation. --- Canonical basis. --- Cartesian product. --- Clifford torus. --- Combinatorics. --- Compact space. --- Conjugacy class. --- Connected space. --- Contact geometry. --- Convex cone. --- Convex hull. --- Coprime integers. --- Coset. --- Covering space. --- Dehn surgery. --- Dense set. --- Diagram (category theory). --- Diameter. --- Diffeomorphism. --- Differential geometry of surfaces. --- Discrete group. --- Double coset. --- Eigenvalues and eigenvectors. --- Equation. --- Equivalence class. --- Equivalence relation. --- Euclidean distance. --- Four-dimensional space. --- Function (mathematics). --- Fundamental domain. --- Geometry and topology. --- Geometry. --- Harmonic function. --- Hexagonal tiling. --- Holonomy. --- Homeomorphism. --- Homology (mathematics). --- Homotopy. --- Horosphere. --- Hyperbolic 3-manifold. --- Hyperbolic Dehn surgery. --- Hyperbolic geometry. --- Hyperbolic manifold. --- Hyperbolic space. --- Hyperbolic triangle. --- Hypersurface. --- I0. --- Ideal triangle. --- Intermediate value theorem. --- Intersection (set theory). --- Isometry group. --- Isometry. --- Limit point. --- Limit set. --- Manifold. --- Mathematical induction. --- Metric space. --- Möbius transformation. --- Parameter. --- Parity (mathematics). --- Partial derivative. --- Partition of unity. --- Permutation. --- Polyhedron. --- Projection (linear algebra). --- Projectivization. --- Quotient space (topology). --- R-factor (crystallography). --- Real projective space. --- Right angle. --- Sard's theorem. --- Seifert fiber space. --- Set (mathematics). --- Siegel domain. --- Simply connected space. --- Solid torus. --- Special case. --- Sphere. --- Stereographic projection. --- Subgroup. --- Subsequence. --- Subset. --- Tangent space. --- Tangent vector. --- Tetrahedron. --- Theorem. --- Topology. --- Torus. --- Transversality (mathematics). --- Triangle group. --- Union (set theory). --- Unit disk. --- Unit sphere. --- Unit tangent bundle.

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Global analysis describes diverse yet interrelated research areas in analysis and algebraic geometry, particularly those in which Kunihiko Kodaira made his most outstanding contributions to mathematics. The eminent contributors to this volume, from Japan, the United States, and Europe, have prepared original research papers that illustrate the progress and direction of current research in complex variables and algebraic and differential geometry. The authors investigate, among other topics, complex manifolds, vector bundles, curved 4-dimensional space, and holomorphic mappings. Bibliographies facilitate further reading in the development of the various studies.Originally published in 1970.The Princeton Legacy Library uses the latest print-on-demand technology to again make available previously out-of-print books from the distinguished backlist of Princeton University Press. These editions preserve the original texts of these important books while presenting them in durable paperback and hardcover editions. The goal of the Princeton Legacy Library is to vastly increase access to the rich scholarly heritage found in the thousands of books published by Princeton University Press since its founding in 1905.

Differential geometry. Global analysis --- Global analysis (Mathematics) --- Calculus of variations --- Differentiable manifolds --- 517.97 --- Analysis, Global (Mathematics) --- Differential topology --- Functions of complex variables --- Geometry, Algebraic --- Calculus of variations. Mathematical theory of control --- Differentiable manifolds. --- Calculus of variations. --- Global analysis (Mathematics). --- 517.97 Calculus of variations. Mathematical theory of control --- Algebraic topology --- 514.7 --- -Calculus of variations --- #TCPW W3.0 --- #TCPW W3.2 --- #WWIS:MEET --- Differential manifolds --- Manifolds (Mathematics) --- Isoperimetrical problems --- Variations, Calculus of --- Maxima and minima --- Differential geometry. Algebraic and analytic methods in geometry --- 514.7 Differential geometry. Algebraic and analytic methods in geometry --- Addresses, essays, lectures --- Functional analysis --- Geometry --- Algebra homomorphism. --- Algebraic space. --- Associated graded ring. --- Automorphism. --- Betti number. --- Bilinear form. --- Canonical basis. --- Canonical bundle. --- Closed immersion. --- Codimension. --- Coefficient. --- Cohomology. --- Cokernel. --- Complete intersection. --- Complex manifold. --- Complex torus. --- Convex cone. --- Covering space. --- Dedekind domain. --- Deformation theory. --- Degenerate bilinear form. --- Diagram (category theory). --- Diffeomorphism. --- Differential form. --- Discrete group. --- Discrete valuation ring. --- Divisor. --- Elliptic operator. --- Elliptic surface. --- Endomorphism. --- Enriques surface. --- Epimorphism. --- Equation. --- Exact sequence. --- Existential quantification. --- Extremal length. --- Fiber bundle. --- Flat morphism. --- Frame bundle. --- Functor. --- Generic point. --- Grassmannian. --- Harmonic function. --- Heine–Borel theorem. --- Hensel's lemma. --- Holomorphic function. --- Homogeneous coordinates. --- Homomorphism. --- Hyperplane. --- Invertible sheaf. --- Kodaira embedding theorem. --- Kodaira vanishing theorem. --- Lie algebra. --- Line bundle. --- Linear independence. --- Linear map. --- Local ring. --- Mathematical induction. --- Meromorphic function. --- Metric space. --- Morphism. --- Natural number. --- Norm (mathematics). --- Normal extension. --- Normal subgroup. --- Open set. --- Orientability. --- Orthonormal basis. --- Partition of unity. --- Polynomial. --- Principal bundle. --- Principal homogeneous space. --- Projection (mathematics). --- Projective line. --- Quadric. --- Rational singularity. --- Residue field. --- Riemannian manifold. --- Ring homomorphism. --- Self-adjoint operator. --- Sheaf (mathematics). --- Sobolev space. --- Special case. --- Stokes' theorem. --- Subgroup. --- Submanifold. --- Subset. --- Subspace theorem. --- Summation. --- Surjective function. --- Symmetric tensor. --- Symplectic vector space. --- Tangent space. --- Theorem. --- Universal bundle. --- Upper and lower bounds. --- Vector bundle. --- Vector field. --- Wirtinger inequality (2-forms). --- Zariski topology. --- Analyse globale (mathématiques) --- Calcul des variations --- Analyse globale (mathématiques) --- Kodaira (kunihiko), mathematicien japonais, 1915 --- -Kodaira (kunihiko), mathematicien japonais, 1915 --- -517.97 --- -Analyse globale (mathématiques) --- -Algebraic topology