Seminar on Differential Geometry. (AM-102), Volume 102 (eBook)

Shing-Tung Yau (Herausgeber)

eBook Download: PDF

2016
720 Seiten
Princeton University Press (Verlag)
978-1-4008-8191-8 (ISBN)

Infos

This collection of papers constitutes a wide-ranging survey of recent developments in differential geometry and its interactions with other fields, especially partial differential equations and mathematical physics. This area of mathematics was the subject of a special program at the Institute for Advanced Study in Princeton during the academic year 1979-1980; the papers in this volume were contributed by the speakers in the sequence of seminars organized by Shing-Tung Yau for this program. Both survey articles and articles presenting new results are included. The articles on differential geometry and partial differential equations include a general survey article by the editor on the relationship of the two fields and more specialized articles on topics including harmonic mappings, isoperimetric and Poincare inequalities, metrics with specified curvature properties, the Monge-Arnpere equation, L2 harmonic forms and cohomology, manifolds of positive curvature, isometric embedding, and Kraumlhler manifolds and metrics. The articles on differential geometry and mathematical physics cover such topics as renormalization, instantons, gauge fields and the Yang-Mills equation, nonlinear evolution equations, incompleteness of space-times, black holes, and quantum gravity. A feature of special interest is the inclusion of a list of more than one hundred unsolved research problems compiled by the editor with comments and bibliographical information.

Produkt-Details

• Erscheint lt. Verlag: 2.3.2016
• Reihe/Serie: Annals of Mathematics Studies
• Reihe/Serie: Annals of Mathematics Studies
• Verlagsort: Princeton
• Sprache: englisch
• Themenwelt: Mathematik / Informatik ► Mathematik ► Geometrie / Topologie
• Schlagworte: Algebraic Curve • analytic function • analytic torsion • Annals of Mathematics • Bochner's theorem • Boundary value problem • Cartan–Hadamard theorem • Cayley–Hamilton theorem • cohomology • Compactification (mathematics) • Continuous function (set theory) • Critical point (mathematics) • Curvature • Cut locus (Riemannian manifold) • Diagram (category theory) • Differential Geometry • Dirac Operator • Disk (mathematics) • Divisor (algebraic geometry) • Duality (mathematics) • Eigenfunction • Eigenvalues and Eigenvectors • Einstein Field Equations • Einstein Manifold • elliptic operator • Equation • Euclidean space • Explicit formulae (L-function) • Exponential map (Riemannian geometry) • First-order partial differential equation • Fixed point (mathematics) • Fubini–Study metric • Function (mathematics) • Gauge Theory • Gauss–Bonnet theorem • Gaussian curvature • Gauss map • Geodesics in general relativity • Geometry • harmonic map • holomorphic function • Homology (mathematics) • Hurewicz theorem • hyperbolic partial differential equation • hypersurface • Inequality (mathematics) • integral equation • Intersection form (4-manifold) • Intersection Homology • Intersection (set theory) • Kähler manifold • Lie algebra • Liouville's theorem (complex analysis) • Liouville's theorem (Hamiltonian) • Mathematical Induction • Mathematical problem • mean value theorem • Measure (mathematics) • Metric connection • Metric Space • Minkowski inequality • Minkowski space • Newton's method • Norm (mathematics) • Parity (mathematics) • partial differential equation • Partition function (mathematics) • Penrose–Hawking singularity theorems • Poincaré conjecture • Pseudo-Riemannian manifold • Quotient space (topology) • Restriction (mathematics) • Ricci curvature • Riemannian manifold • Riemann sphere • Riemann surface • Ring (mathematics) • scalar curvature • Schwarz lemma • Schwarzschild metric • sectional curvature • Sheaf (mathematics) • Sign (mathematics) • Sine-Gordon Equation • Sphere theorem • Sphere theorem (3-manifolds) • Stokes' theorem • Support (mathematics) • Surface (topology) • Symplectic Geometry • Theorem • Topological quantum number • Trace (linear algebra) • uniformization theorem • uniqueness theorem • Variable (mathematics) • Yang–Mills Theory
• ISBN-10: 1-4008-8191-9 / 1400881919
• ISBN-13: 978-1-4008-8191-8 / 9781400881918