Published on *Max-Planck-Institut für Mathematik* (http://www.mpim-bonn.mpg.de)

Posted in

- Vortrag [1]

Speaker:

Asma Hassannezhad
Zugehörigkeit:

University of Bristol
Datum:

Don, 2019-02-07 16:30 - 17:30 The Dirichlet-to-Neumann operator is a first order elliptic pseudodifferential operator. It acts on smooth functions on the boundary of a Riemannian manifold and maps a function to the normal derivative of its harmonic extension. The eigenvalues of the Dirichlet-to-Neumann map are also called Steklov eigenvalues. It has been known that the geometry of the boundary has a strong influence on the Steklov eigenvalues. In this talk, we show that for every $k$, the $k$th Steklov eigenvalue is comparable to the square root of the $k$th Laplace eigenvalue. This result, in particular, gives a two-sided geometric bound for any Steklov eigenvalue which depends only on the geometry near the boundary. This is joint work with Bruno Colbois and Alexandre Girouard.

**Links:**

[1] http://www.mpim-bonn.mpg.de/de/taxonomy/term/39

[2] http://www.mpim-bonn.mpg.de/de/node/3444

[3] http://www.mpim-bonn.mpg.de/de/node/4652