Geometria em Lisboa Seminar  

03/06/2019, 15:00 — 16:00 — Room P3.10, Mathematics BuildingInstituto Superior Técnicohttp://tecnico.ulisboa.pt
Richard Laugesen, University of Illinois at Urbana-Champaign

Spectrum of the Robin Laplacian: recent results, and open problems

I will discuss two recent theorems and one recent conjecture about maximizing
or minimizing the first three eigenvalues of the Robin Laplacian of a simply
connected planar domain. Conformal mappings and winding numbers play a key
role in the geometric constructions. In physical terms, these eigenvalues
represent decay rates for heat flow assuming a “partially insulating” boundary.