# Introductory seminar: Extremal metrics for the ground state and minimal immersions into spheres

Rosa Sena-Dias
(IST, Lisbon)
Student Seminar
Tuesday, 10 April, 2018, at 16:15-17:00, in G3.3 (1532-322)
Abstract:

In the 60's, Hersch showed that the round metric on $S^2$ maximizes the first eigenvalue among all metrics of normalised volume and opened up a question which has become popular: given a Riemann surface, are there extremal metrics for the first eigenvalue and if so what are they?

In the 90's Nadirashvili used variational methods to formulate and address this question on the $2$-torus. In the process he found a connection between those metrics which are critical for $\lambda_1$ and minimal immersions into spheres. This relation was extended to all Riemannian manifolds by El Soufi and Ilias. Our goal is to discuss their results by formulating the relation precisely and explaining why critical metrics yield minimal immersions.

This seminar gives an introduction to "The research seminar by Rosa Sena-Dias. The seminar is meant for Master and PhD students.

Organised by: QGM
Contact person: Cristiano Spotti, Martin de Borbon & Roberta Iseppi