Mathematische Gesellschaft am 16.2.2012
Donnerstag, 16.02.2012
Ma Li, z. Z. Göttingen
Ricci flow in dimension two
Abstract:
The Ricci flow is a well-known tool in the Mathematical
society because of the resolution of 3-d Poincare conjecture. The Ricci
flow is invented by R.Hamilton. The topic of my talk is about the Ricci
flow in dimension two, which is a conformal flow. I shall start from the
brief review about the definition of Gauss curvature and some basic
formula. Considered as conformal metrics, the flow can be reduced to a
single evolution equation. From here, one can see the local existence of
the flow with the given initial data. In 2-d, any Riemannian metric is
Kaehler and then the flow can be formulated as the Kaehler-Ricci flow.
Based on these formulations, I shall discuss some recent results of the
2-d Ricci flow and interesting arguments involved. I shall also
mentioned some open questions.