printable pdf
比利时vs摩洛哥足彩 ,
university of california san diego

****************************

differential geometry seminar

brett kotschwar

max planck institute for gravitational physics, potsdam

ricci flow and the holonomy group

abstract:

i will discuss a "non-contraction" result for the holonomy group of a solution to ricci flow, namely, that if the reduced holonomy of a complete solution of uniformly bounded curvature is restricted to a subgroup of so(n) at some non-initial time, it must be restricted to the same subgroup at all previous times; it follows then from existing results that the holonomy group is exactly preserved by the equation. in particular, a solution may be kahler or locally reducible (as a product) on some time slice only if it is identically so on its entire interval of existence. in contrast to the question of "non-expansion" of holonomy, the problem of non-contraction cannot be reduced completely to an application of the classification and splitting theorems of berger and de rham and a series of appeals to a relevant uniqueness theorem (here, backwards-uniqueness). however, with an infinitesimal reformulation, we show that the problem can nevertheless be reduced to one of unique continuation, and specifically to one for a coupled system of partial- and ordinary-differential inequalities of a form amenable to an approach by carleman inequalities. this reformulation also leads to an alternative and essentially self-contained proof of the non-expansion of holonomy via the analysis of a similar (albeit simpler and strictly parabolic) system by means of the maximum principle.

host: lei ni

april 13, 2011

4:00 pm

ap&m 5402

****************************