Seminario

Data evento: 
Martedì, 19 Luglio, 2016 - 15:00

Seminario di Geometria

Aula 1E (pal. RM004)

Mikhail Karpukhin (Mc Gill University, Montreal)

Upper bounds for Steklov eigenvalues via conjugate harmonic forms
 

Abstract:

In 1975 Hersch, Payne and Schiffer used the concept of conjugate harmonic functions on the complex plane to prove a sharp upper bound for Steklov eigenvalues on simply connected domains. In this talk we will discuss a higher dimensional version of this concept defined for an arbitrary Riemannian manifold with boundary-conjugate harmonic forms. As a result, an inequality relating Steklov eigenvalues of the manifold with the Laplace eigenvalues of the boundary is obtained. This inequality is reduced to Hersch-Payne-Schiffer inequality in the case of simply connected domains and yields improved upper bounds even in a two-dimensional case.