Algebraic curve
Analytic function
Analytic torsion
Bochner's theorem
Cartan-Hadamard theorem
Category=PBMP
Compactification (mathematics)
Continuous function (set theory)
Critical point (mathematics)
Curvature
Cut locus (Riemannian manifold)
Differential geometry
Dirac operator
Disk (mathematics)
Divisor (algebraic geometry)
Duality (mathematics)
Eigenvalues and eigenvectors
Einstein field equations
Einstein manifold
Elliptic operator
eq_isMigrated=1
eq_isMigrated=2
eq_nobargain
Equation
Explicit formulae (L-function)
Exponential map (Riemannian geometry)
First-order partial differential equation
Fixed point (mathematics)
Fubini-Study metric
Function (mathematics)
Geometry
Harmonic map
Holomorphic function
Homology (mathematics)
Hyperbolic partial differential equation
Hypersurface
Integral equation
Intersection (set theory)
Kahler manifold
Lie algebra
Liouville's theorem (complex analysis)
Liouville's theorem (Hamiltonian)
Mathematical induction
Mathematical problem
Minkowski inequality
Minkowski space
Newton's method
Norm (mathematics)
Parity (mathematics)
Partial differential equation
Partition function (mathematics)
Penrose-Hawking singularity theorems
Pseudo-Riemannian manifold
Restriction (mathematics)
Ricci curvature
Riemann sphere
Riemann surface
Riemannian manifold
Ring (mathematics)
Scalar curvature
Schwarz lemma
Sectional curvature
Sheaf (mathematics)
Sign (mathematics)
Sine-Gordon equation
Stokes' theorem
Support (mathematics)
Surface (topology)
Symplectic geometry
Theorem
Trace (linear algebra)
Uniformization theorem
Variable (mathematics)
Yang-Mills theory
Product details
- ISBN 9780691082967
- Weight: 1021g
- Dimensions: 152 x 229mm
- Publication Date: 21 Mar 1982
- Publisher: Princeton University Press
- Publication City/Country: US
- Product Form: Paperback
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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.
