I will describe some constructions of solutions to some semilinear elliptic equations, all of which are based on the understanding of minimal and constant mean curvature surfaces in Euclidean space. For example, I will explain the role of minimal surfaces in the construction of entire solutions of the Allen-Cahn equation in ℝn, I will also present the construction of solutions for some overdetermined elliptic problems which arise in the study of extremal domains for the first eigenvalue of the Laplacian.

I will describe some constructions of solutions to some semilinear elliptic equations, all of which are based on the understanding of minimal and constant mean curvature surfaces in Euclidean space. For example, I will explain the role of minimal surfaces in the construction of entire solutions of the Allen-Cahn equation in ℝn, I will also present the construction of solutions for some overdetermined elliptic problems which arise in the study of extremal domains for the first eigenvalue of the Laplacian.

I will describe some constructions of solutions to some semilinear elliptic equations, all of which are based on the understanding of minimal and constant mean curvature surfaces in Euclidean space. For example, I will explain the role of minimal surfaces in the construction of entire solutions of the Allen-Cahn equation in ℝn, I will also present the construction of solutions for some overdetermined elliptic problems which arise in the study of extremal domains for the first eigenvalue of the Laplacian.