Event Type:

Analysis Seminar

Date/Time:

Monday, February 29, 2016 - 12:00 to 13:00

Location:

GILK 115

Guest Speaker:

Institution:

University of Oregon

Abstract:

Schiffers conjecture states that if Neumann eigenfunction is constant on the boundary of a domain, then the domain is a disk, or the eigenfunction is constant. The disk is special, due to the presence of radial modes. We will discuss existence of Neumann modes on regular polygons and boxes which are nearly radial (do not change sign on the boundary). We will build on the following recent result of Hoffmann-Ostenhof: an eigenfunction of a rectangle that is strictly positive on the boundary must be constant.