Convergence of Calabi–Yau manifolds
By Wei-Dong Ruan, Yuguang Zhang. 2009
50 citations recorded by the source corpus.
Abstract In this paper, we study the convergence of Calabi–Yau manifolds under Kahler degeneration to orbifold singularities and complex degeneration to canonical singularities (including the conifold singularities), and the collapsing of a family of Calabi–Yau manifolds.
Subfields: Applied Mathematics, Geometry and Topology
View Paper: https://www.semanticscholar.org/paper/1389b155616504c9617372888079222caad6b693
How researchers see this paper
The researchers whose trusted networks rank it highest, strongest advocate first. Every researcher gets a different order.
In Applied Mathematics
- Valentino Tosatti
- Xiaokui Yang
- B. Weinkove
- Yuguang Zhang
- Mark Gross
- G'abor Sz'ekelyhidi
- Duong H. Phong
- Jian Song
In Geometry and Topology
- Valentino Tosatti
- Xiaokui Yang
- B. Weinkove
- Yuguang Zhang
- Mark Gross
- G'abor Sz'ekelyhidi
- Duong H. Phong
- Jian Song
Citations in the corpus
- The Kähler-Ricci flow, Ricci-flat metrics and collapsing limits (2014, background): “By comparison, in the case when the volume of the Ricci-flat metrics is non-collapsing, we have a very thorough understanding of their limiting behavior, thanks to the results in [8, 31, 32, 33, 37, 53], and all the analogous questions have affirmative answers.”
- Gromov-Hausdorff collapsing of Calabi-Yau manifolds (2013, result): “In the case of non-collapsing limits, analogous results about metric completions have been obtained in [25, 26, 27], and homeomorphism results have been obtained in [6] (see also [33]).”
- Collapsing of abelian fibred Calabi-Yau manifolds (2011, background): “The general question of understanding the geometric behaviour of these metrics was raised by Yau [46, 47], Wilson [44] and others, and much work has been devoted to it, see for example [18, 29, 30, 34, 37, 38] and references therein.”