Teacher: Stefano Montaldo – montaldo@unica.it – tel. 070/6758539

Suitable for: Student of the bachelor degree in mathematics

CFU=4

What is needed : Geometria 4.

Content. A surface whose mean curvature is constant but not equal to 0 is obtained when we minimize the area of a surface while preserving its volume; the sphere is a trivial example and the constant mean curva­ture torus discovered by H. Wente in 1984 gave geometers a powerful incentive to study such surfaces. Subsequently, many constant mean curvature surfaces were discovered using a variety of techniques. In this reading, we aim to explain various examples of constant mean curvature surfaces and the techniques for studying them.

In particular the reading is focused on Chapters 1,2,3,4,6 of the book:

Kenmotsu, Katsuei, Surfaces with constant mean curvature. Translated from the 2000 Japanese original by Katsuhiro Moriya and revised by the author. Translations of Mathematical Monographs, 221. American Mathematical Society, Providence, RI, 2003.

Structure of the reading: for each academic year the reading course is divided as follows:

• in the first part the teacher will give some lectures introducing the topics of the course (4 hours per academic year);
• in the second part the students will improve their knowledge of the course contents, meeting the teacher periodically for clarification (20 hours per academic year).

Final exam: The exam takes place on the blackboard through the presentation of a topic chosen by the student followed by some questions from the teacher.