Tuesday, September 15, 2009
10:30 AM in REC 307
Professor Bartek Siudeja
University of Illinois at Urbana Champaign

Sharp bounds for Neumann eigenvalues of triangles

Abstract

Among all triangles with fixed diameter, we prove the degenerate acute isosceles triangle minimizes the Neumann fundamental tone. In the other direction, if we fix perimeter (or area) then the equilateral triangle maximizes the Neumann fundamental tone. Our approach involves variational principles and geometric transformations of the domain. We also prove symmetry/antisymmetry for eigenfunctions of isosceles triangles.