[institut] predavanje, ponedeljak 8.maj

[Odeljenje za mehaniku]

Postovane kolege,

Iduce nedelje imamo uvazenog gosta sa Moskovskog drzavnog univerziteta.
Predavanje ce se odrzati, umesto u sredu, u ponedeljak 8. maja.

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Zajednicka sednica Odeljenja za mehaniku i matematiku Matematickog 
instituta SANU

Ponedeljak 8. maj, u 14 sati i 15 minuta
Teodor Popelenski (Moskva, Met-Mah)

On combinatorial Ricci flow on surfaces

After R.Hamilton's paper (1982) Three-manifolds with positive Ricci
curvature natural question the natural question about properties of
the Ricci flow on surfaces arised. In this dimension the long-time
existence and convergence were proved more or less easy: in 1986
R.Hamilton announced and in  1988 published the proof of convergence
of the Ricci flow to the metric of constant curvature for arbitrary
initial metric for any closed surface different form the sphere;  in
1991 B.Chow closed the question by proving the same statement for
twodimentional sphere.

In 2003 B.Chow and F.Luo investigated on of possible "disctetization"
of the Ricce flow. Fixed data consists of a closed surface, its
triangulation, and weights on the edges of the triangulations. For
this object one has so called "circle packing metrics", corresponding
curvatures, and  Ricci flow. This version of discretiazation is
important due to the circle packings which were investigated by
Thurston in his unpublished book "Geometry and topology of
3-manifolds."

Chow and Luo showed that under certian conditions on the weight
function the Ricci flow converges exponentially fast to the metric of
constant curvature. One of the important conditions consists in
nonnegativity of the weights.

Recently R.Pepa and me were able to weaken some of the Clow-Luo
conditions. Namely some weights can be negative but still should
satisfy some conditions. Also we show that the weakening the
conditions cannot be unlimited. We found examples of triangulation of
surfaces and weights on the edges of the triangulation such that there
exists saddle points of the Ricci flow.

In the talk I give the exposition of old results and present some new 
ones.


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Sekretar Odeljenja za mehaniku
dr Katarina Kukic