Minicurso - 6 aulas

I propose to give a 3 week mini-course on the subject of minimal and constant mean curvature surfaces at IMPA during January 2015. In the first week of the course I plan to cover the standard material in the classical theory of minimal surfaces in R3; for the most part this is the more standard material covered in the first half of my joint book [4] with Joaquin Perez. During the second week of the course I will focus my attention on the classical theory of constant mean curvature H > 0 surfaces in R3; this is in contrast to the material in the first week of the course where the mean curvature of the surfaces being considered is assumed H = 0. The material of second week is again the standard material in this subject with an emphasis on the special case of embedded (H > 0)-surfaces in R3 as well possibly some more recent work on curvature estimates for (H > 0)-disks by Meeks and Tinaglia. In each of these first 2 weeks of the course I will include some nontrivial classical global results such as the characterization of ends of H-surfaces with H > 0 as being asymptotic to the ends of Delaunay surfaces of revolution. In the third week of the course I will focus on the study of embedded H-surfaces in Riemannian 3 manifolds N with an emphasis on the case where N is homogeneous; see my joint article [3] with Joaquin Pérez for some of this last material and also the closely related articles [1, 2]. I hope to have some preliminary lecture notes and slides of lectures available to course participants before the course begins.