Complete Kähler manifolds with zero Ricci curvature. I
Gang Tian,Shing-Tung Yau +1 more
About:
This article is published in Journal of the American Mathematical Society.The article was published on 1990-07-01 and is currently open access. It has received 339 citations till now. The article focuses on the topics: Ricci-flat manifold & Curvature of Riemannian manifolds.read more
Citations
More filters
Journal ArticleDOI
CFT's from Calabi–Yau four-folds
TL;DR: In this article, the authors consider F/M/Type IIA theory compactified to four, three, or two dimensions on a Calabi-Yau fourfold, and study the behavior near an isolated singularity in the presence of appropriate fluxes and branes.
Journal ArticleDOI
Compact Riemannian 7-manifolds with holonomy G2. II
TL;DR: In this paper, the authors explore the theory of compact Riemannian 7-manifolds with holonomy G2 in greater detail and give a number of open problems.
Journal ArticleDOI
K‐Stability and Kähler‐Einstein Metrics
Gang Tian,Gang Tian +1 more
TL;DR: In this paper, it was shown that if a Fano manifold M is K-stable, then it admits a Kahler-Einstein metric (see Section 2.2.1).
Gauge dynamics and compactification to three-dimensions
Nathan Seiberg,Edward Witten +1 more
TL;DR: In this article, the authors studied four dimensional supersymmetric gauge theories on a circle of radius ρ with a radius of ρ, and showed that the vacuum structure can be determined quite precisely as a function of the radius of the circle.
References
More filters
Book
Elliptic Partial Differential Equations of Second Order
David Gilbarg,Neil S. Trudinger +1 more
TL;DR: In this article, Leray-Schauder and Harnack this article considered the Dirichlet Problem for Poisson's Equation and showed that it is a special case of Divergence Form Operators.
Journal ArticleDOI
On The Ricci Curvature of a Compact Kahler Manifold and the Complex Monge-Ampere Equation, I*
TL;DR: In this paper, the Ricci form of some Kahler metric is shown to be closed and its cohomology class must represent the first Chern class of M. This conjecture of Calabi can be reduced to a problem in non-linear partial differential equation.
Book
Compact Complex Surfaces
TL;DR: In this article, the authors describe the topology and algebraic properties of complex surfaces, including the following properties: 1. The Projective Plane, 2. The Jacobian Fibration, 3. Hodge Theory on Surfaces, 4. Inequahties for Hodge Numbers, 5. Holomorphic Vector Bundles, Serre Duality and Riemann-Roch Theorem.