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RESEARCH BLOG 5/19/03 Dan Knopf notified me that he has a survey paper (on which his talk
 

Summary: RESEARCH BLOG 5/19/03
Dan Knopf notified me that he has a survey paper (on which his talk
at UIC was based) on models of singularities in the Ricci flow (see his
web page).
I've been thinking about the conjectures made in research blog 3/4/03,
specifically conjecture 2 about backwards propagation of minimal sur-
faces under Ricci flow, and conjecture 4 that in a bumpy metric, there
are only finitely many disjoint embedded minimal 2-spheres (actually,
I would rather know this for real-analytic Riemannian metrics, since
under Ricci flow, the metric becomes instantaneously analytic). I'll
review Hamilton's formula for the variation of area of minimal surfaces
under Ricci flow, then I'll explain my strategy for attempting to prove
the above two conjectures.
The following is an expanded version of pp. 40-41 of Hamilton's paper
[3]. Consider a co-oriented surface 2
in a Riemannian 3-manifold M3
with metrics (M, gt) satisfying the Ricci flow
tgt = -2Ric(gt). At each
point x , choose an orthonormal frame for g0 {e1, e2, N}, where ei
Tx and N gives the coorientation (we will suppress the dependence

  

Source: Agol, Ian - Department of Mathematics, Statistics, and Computer Science, University of Illinois at Chicago

 

Collections: Mathematics