Complex Monge-Ampère of a maximum

We derive a formula for where is a finite maximum. As an application, we compute the complex equilibrium measures of some generalized polyhedra.

     

Transfinite Diameter with Generalized Polynomial Degree

Potential Analysis - We prove a Chebyshev transform formula for a notion of (weighted) transfinite diameter that is defined using a generalized notion of polynomial degree. We also generalize Leja...     

Monge–Ampère of Pac-Man

We show that the Monge–Ampère density of the extremal function $$V_P$$ for a non-convex Pac-Man set $$P\subset {{\mathbb {R}}}^2$$ tends to a finite limit as we approach the vertex p of P along lines but with a value that may vary with the line. On the other hand, along a tangential approach to p, the Monge–Ampère density becomes unbounded. This partially mimics the behavior of the Monge–Ampère density of the union of two quarter disks S of Sigurdsson and Snaebjarnarson (Ann Pol Math 123:481–504, 2019). We also recover their formula for $$V_S$$ by elementary methods.