90 research outputs found
Pluriclosed flow on generalized K\"ahler manifolds with split tangent bundle
We show that the pluriclosed flow preserves generalized K\"ahler structures
with the extra condition , a condition referred to as "split
tangent bundle." Moreover, we show that in this in this case the flow reduces
to a nonconvex fully nonlinear parabolic flow of a scalar potential function.
We prove a number of a priori estimates for this equation, including a general
estimate in dimension of Evans-Krylov type requiring a new argument due
to the nonconvexity of the equation. The main result is a long time existence
theorem for the flow in dimension , covering most cases. We also show that
the pluriclosed flow represents the parabolic analogue to an elliptic problem
which is a very natural generalization of the Calabi conjecture to the setting
of generalized K\"ahler geometry with split tangent bundle.Comment: to appear Crelle's Journa
Pluriclosed flow on manifolds with globally generated bundles
We show global existence and convergence results for the pluriclosed flow on
manifolds for which certain naturally associated tensor bundles are globally
generated
Ricci Yang-Mills flow on surfaces
We study the behaviour of the Ricci Yang-Mills flow for U(1) bundles on
surfaces. We show that existence for the flow reduces to a bound on the
isoperimetric constant. In the presence of such a bound, we show that on ,
if the bundle is nontrivial, the flow exists for all time. For higher genus
surfaces the flow always exists for all time. The volume normalized flow always
exists for all time and converges to a constant scalar curvature metric with
the bundle curvature parallel. Finally, in an appendix we classify all
gradient solitons of this flow on surfaces
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