15 research outputs found
On the Blaschke-Lebesgue theorem for the Cheeger constant via areas and perimeters of inner parallel sets
The first main result presented in the paper shows that the perimeters of
inner parallel sets of planar shapes having a given constant width are minimal
for the Reuleaux triangles. This implies that the areas of inner parallel sets
and, consequently, the inverse of the Cheeger constant are also minimal for the
Reuleaux triangles. Proofs use elementary geometry arguments and are based on
direct comparisons between general constant width shapes and the Reuleaux
triangle
Low Eigenvalues of Laplace and Schrödinger Operators
This workshop brought together researchers interested in eigenvalue problems for Laplace and Schr¨dinger operators. The main topics o of discussions and investigations covered Dirichlet and Neumann eigenvalue problems, inequalities for the spectral gap, isoperimertic problems and sharp Lieb–Thirring type inequalities. The focus included not only the analytic and geometric sides of the problems, but also related probabilistic and computational aspects