The monotonicity trick and applications
7-11 Nov 2022
We discuss the analytic basis of the "monotonicity trick'' and present applications in several fields.
These range from the analysis of Ginzburg-Landau vortices over finding multi-vortex solutions in Chern-Simons gauge theory to showing existence of vortex rings in an ideal fluid.
If time permits, we will conclude by showing how the "monotonicity trick'' permits to bound the total absolute curvature of conformal metrics on closed surfaces of higher genus having prescribed Gauss curvature of changing sign.