The Yang-Mills gradient flow in four dimensions
Prompted by recent work of Xiuxiong Chen, a unified approach to the Hamilton-Ricci and Calabi flows on a closed, compact surface is presented, recovering global existence and exponentially fast asymptotic convergence from concentration-compactness results for conformal metrics.
For semilinear elliptic equations of critical exponential growth we establish the existence of positive solutions to the Dirichlet problem on suitable non-contractible domains.
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