An elementary introduction to eigenvalue problems with an application to catenoids in $R^3$

Pierre Bérard (1)

1 IF - Institut Fourier

These notes are intended for geometry students and they aim at giving an elementary introduction to eigenvalue problems based on variational methods (min-max principle). The Sturm-Liouville Dirichlet eigenvalue problem over a compact interval is treated, with an application to the stability of domains on the catenoid in the euclidean space.

Mots clés: Eigenvalue problems; Sturm-Liouville problem; Stability

Domaines: Géométrie différentielle [math.DG]

Pierre Bérard. An elementary introduction to eigenvalue problems with an application to catenoids in $R^3$. XV Escola de geometria diferencial. IMPA - Instituto nacional de matematica pura e aplicada, Rio de Janeiro (Brasil), pp.52, 2008. ⟨hal-00357710⟩