Richard M. Schoen, Lecture II: Two eigenvalue problems for surfaces

Speaker: Richard M. Schoen, Distinguished Professor and Excellence in Teaching Endowed Chair University of California, Irvine

Lecture II: Two eigenvalue problems for surfaces
The problem of finding surface geometries (metrics) of a given area which maximize their lowest eigenvalue has been studied for over 50 years. Despite some spectacular successes the problem is still not well understood for most surfaces. In this colloquium lecture we will describe this question and the results which have been obtained. We will also describe a related problem for surfaces with boundary. Both of these questions lead to geometric descriptions of extremal metrics as minimal surfaces and thus lead to a new set of minimal surfaces questions.