The Kähler–Ricci flow on Hirzebruch surfaces
By Jian Song, B. Weinkove. 2009
76 citations recorded by the source corpus.
Abstract We investigate the metric behavior of the Kähler–Ricci flow on the Hirzebruch surfaces, assuming the initial metric is invariant under a maximal compact subgroup of the automorphism group. We show that, in the sense of Gromov–Hausdorff, the flow either shrinks to a point, collapses to or contracts an exceptional divisor, confirming a conjecture of Feldman–Ilmanen–Knopf. We also show that similar behavior holds on higher-dimensional analogues of the Hirzebruch surfaces.
Subfields: Applied Mathematics, Geometry and Topology
View Paper: https://www.semanticscholar.org/paper/dad535d0c1cfea4e2e172486f996189bf432f75c
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
- G'abor Sz'ekelyhidi
- Jian Song
- Duong H. Phong
- G. Tian
- Yuguang Zhang
In Geometry and Topology
- Valentino Tosatti
- Xiaokui Yang
- B. Weinkove
- G'abor Sz'ekelyhidi
- Jian Song
- Duong H. Phong
- G. Tian
- Yuguang Zhang
Citations in the corpus
- The Kähler-Ricci flow, Ricci-flat metrics and collapsing limits (2014, methodology): “According to the analytic minimal model program [39, 40, 41, 50] the Kähler-Ricci flow will perform a surgery at each finite time singularity, corresponding to a birational operation of the minimal model program from algebraic geometry, and arrive at the minimal model Xmin with nef canonical bundle ”
- The Kähler–Ricci flow through singularities (2009, background): “It is further shown in [34,35] that the Kähler–Ricci flow is extended through the singular time continuously in Gromov–Hausdorff topology.”