Essays about: "Minkowski dimension"

Found 2 essays containing the words Minkowski dimension.

1. 1. Three Perspectives of Schiemann’s Theorem

   University essay from Göteborgs universitet/Institutionen för matematiska vetenskaper

   Author : Felix Rydell; [2020-06-23]
   Keywords : Lattice theory; Minkowski reduction; flat torus; isospectrality; spectral determination; positive definite quadratic forms; Alexander Schiemann.;

   Abstract : Interest in the field of spectral geometry, the study of how analytic and geometric properties of manifolds are related, was sparked when Marc Kac in 1966 asked the question “can one hear the shape of a drum?”. One of the problems that garnered attention because of this was whether the Laplace spectrum of a flat torus determines its shape, even though it was not new. READ MORE

3. 2. Fractal sets and dimensions

   University essay from Matematiska institutionen

   Author : Patrik Leifsson; [2006]
   Keywords : box dimension; Cantor dust; Cantor set; dimension; fractal; Hausdorff dimension; measure; Minkowski dimension; packing dimension; Sierpinski gasket; similarity; space-filling curve; topological dimension; von Koch curve;

   Abstract : Fractal analysis is an important tool when we need to study geometrical objects less regular than ordinary ones, e.g. a set with a non-integer dimension value. It has developed intensively over the last 30 years which gives a hint to its young age as a branch within mathematics. READ MORE