Scalar Curvature Behavior for Finite Time Singularity of K

By Zhou Zhang. 2009

91 citations recorded by the source corpus.

In this short paper, we show that K\"ahler-Ricci flows over closed manifolds would have scalar curvature blown-up for finite time singularity. Certain control of the blowing-up is achieved with some mild assumption.

Subfields: Applied Mathematics, Geometry and Topology, Nuclear and High Energy Physics

View Paper: https://www.semanticscholar.org/paper/6b5c3386d10dd71366468eb6897b787cfe671149

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

1. Valentino Tosatti
2. Jian Song
3. B. Weinkove
4. G'abor Sz'ekelyhidi
5. Tristan C. Collins
6. Xiaokui Yang
7. G. Tian
8. Chi Li

In Geometry and Topology

1. Valentino Tosatti
2. Jian Song
3. B. Weinkove
4. G'abor Sz'ekelyhidi
5. Tristan C. Collins
6. Xiaokui Yang
7. G. Tian
8. Chi Li

In Nuclear and High Energy Physics

1. Valentino Tosatti
2. Tristan C. Collins
3. G. Tian
4. Jian Song
5. Fang Zheng
6. Quanting Zhao

Citations in the corpus

• The Kähler–Ricci flow through singularities (2009, background): “On the other hand, the scalar curvature will in general blow up if the Kähler–Ricci flow develops finite time singularities (see [52]).”
• KAWA lecture notes on the Kähler-Ricci flow (2015, background): “3) holds for all finite time singularities of the Kähler-Ricci flow, but see [92] for partial results.”
• Kähler currents and null loci (2013, background): “Note also that in this setup, Zhang [66] proved that the Ricci curvature of ω(t) must be unbounded from below on X as t → T−.”