Blow-up analysis of conformal metrics of the disk with prescribed Gaussian and geodesic curvatures

This paper is concerned with the compactness of metrics of the disk with prescribed Gaussian and geodesic curvatures. We consider a blowing-up sequence of metrics and give a precise description of its asymptotic behavior. In particular, the metrics blow-up at a unique point on the boundary and we are able to give necessary conditions on its location. It turns out that such conditions depend locally on the Gaussian curvatures but they depend on the geodesic curvatures in a nonlocal way. This is a novelty with respect to the classical Nirenberg problem where the blow-up conditions are local, and this new aspect is driven by the boundary condition.Comment: 31 pages, 1 figur

Risk aversion and debt maturity structure

We study the relationship of risk aversion and debt maturity structure. In a model in which adverse selection in financial markets creates a role for the use of short-term debt, we allow the possibility of borrowers being risk-averse. This creates a trade-off between reduced expected financing costs and higher risk and allows for the study of the effect of risk aversion on optimal maturity structure. We prove that, as risk aversion increases, so does the percentage of debt that is long-term.risk aversion, debt maturity structure, adverse selection.