Let E be a hermitian complex vector bundle over a compact Kähler surface X with Kähler form ω, and let D be an integrable unitary connection on E defining a holomorphic structure D ′′ on E. We prove that the Yang-Mills flow on (X, ω) with initial condition D converges, in an appropriate sense which takes into account bubbling phenomena, to the double dual of the graded sheaf associated to the ω-Harder-Narasimhan-Seshadri filtration of the holomorphic bundle (E, D ′′ ). This generalizes to Kähler surfaces the known result on Riemann surfaces and proves, in this case, a conjecture of Bando and Siu.

induce similar increases in fetal blood pressure and similar falls in the incidence of fetal breathing movements. The pronounced betamethasone-induced fetal hypertension is associated with an increase in fetal femoral vascular resistance.Antenatal glucocorticoid administration to enhance fetal periventricular haemorrhage and necrotizing enterocolitis lung maturation has been used in obstetric practice over the (Crowley, Chalmers & Keirse, 1990). Thus, the National last 20 years since first reported by Liggins (1969). In Institutes of Health recently advised routine administration addition to the well-known decrease in Respiratory in two to four doses for 48 h of either betamethasome or Distress Syndrome, antenatal administration of either beta-dexamethasone to all pregnant women at risk of premature methasone or dexamethasone, the only two glucocorticoids delivery before 32 weeks of gestation (NIH Consensus used clinically, reduces the incidence of neonatal mortality, Development Conference, 1994).

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This paper contains two main results. The first is the existence of an equivariant Weil-Petersson geodesic in Teichmüller space for any choice of pseudo-Anosov mapping class. As a consequence one obtains a classification of the elements of the mapping class group as Weil-Petersson isometries which is parallel to the Thurston classification. The second result concerns the asymptotic behavior of these geodesics. It is shown that geodesics that are equivariant with respect to independent pseudo-Anosov's diverge. It follows that subgroups of the mapping class group which contain independent pseudo-Anosov's act in a reductive manner with respect to the Weil-Petersson geometry. This implies an existence theorem for equivariant harmonic maps to the metric completion.

Two compactifications of the space of holomorphic maps of fixed degree from a compact Riemann surface to a Grassmannian are studied. It is shown that the Uhlenbeck compactification has the structure of a projective variety and is dominated by the algebraic compactification coming from the Grothendieck Quot Scheme. The latter may be embedded into the moduli space of solutions to a generalized version of the vortex equations studied by Bradlow. This gives an effective way of computing certain intersection numbers (known as “Gromov invariants”) on the space of holomorphic maps into Grassmannians. We carry out these computations in the case where the Riemann surface has genus one.