Nonlinear Partial Differential Equations Arising from Prescribed Curvature Problems

Abstract

We consider two prominent nonlinear partial differential equations (nonlinear PDE) linked to the prescribed curvature problems, namely, the Minkowski problem and the Kazdan-Warner/Nirenberg problem (prescribed scalar curvature problem). This article addresses some of the modern techniques in analysis used to draw out a number of the profound features in these equations.