Year: 2019
Type: preprint
Abstract: We show that the first eigenvalue of a closed Riemannian surface normalized by the area can be strictly increased by attaching a cylinder or a cross cap. As a consequence we obtain the existence of maximizing metrics for the normalized first eigenvalue on any closed surface of fixed topological type. Since these metrics are induced by (possibly branched) minimal immersions into spheres, we find new examples of immersed minimal surfaces in spheres.
Source: arXiv (Cornell University)
Authors: Matthiesen, Henrik, Siffert, Anna
Institutions: University of Chicago, Max Planck Institute for Mathematics
Language: English
Subfield: Applied Mathematics
Field: Mathematics
Domain: Physical Sciences
Open Access status: green
OpenAlex ID: W2972029812