26 citations · 84 across the 12 of their papers we have counts for
12 papers
On the geometry of generalised Koch snowflakes
Sven van Golden, Sabrina Kombrink, Tony Samuel
We consider the geometry of a class of fractal sets in that generalise the famous Koch curve and Koch snowflake. While the classical Koch curve is defined by an it…
Dimensions of infinitely generated self-affine sets and restricted digit sets for signed Lüroth expansions
S. van Golden, C. Kalle, S. Kombrink +1
For countably infinite IFSs on consisting of affine contractions with diagonal linear parts, we give conditions under which the affinity dimension is an upper bound f…
Eigenvalue counting functions and parallel volumes for examples of fractal sprays generated by the Koch snowflake
Sabrina Kombrink, Lucas Schmidt
We apply recent results by the authors to obtain bounds on remainder terms of the Dirichlet Laplace eigenvalue counting function for domains that can be realised as countable disjo…
On bounds for the remainder term of counting functions of the Neumann Laplacian on domains with fractal boundary
Sabrina Kombrink, Lucas Schmidt
We provide a new constructive method for obtaining explicit remainder estimates of eigenvalue counting functions of Neumann Laplacians on domains with fractal boundary. This is don…
Lattice self-similar sets on the real line are not Minkowski measurable
Sabrina Kombrink, Steffen Winter
We show that any nontrivial self-similar subset of the real line that is invariant under a lattice iterated function system (IFS) satisfying the open set condition (OSC) is not Min…
Minkowski measurability of infinite conformal graph directed systems and application to Apollonian packings
Marc Kesseböhmer, Sabrina Kombrink
We give conditions for the existence of the Minkowski content of limit sets stemming from infinite conformal graph directed systems. As an application we obtain Minkowski measurabi…
A complex Ruelle-Perron-Frobenius theorem for infinite Markov shifts with applications to renewal theory
Mark Kesseböhmer, Sabrina Kombrink
We prove a complex Ruelle-Perron-Frobenius theorem for Markov shifts over an infinite alphabet, whence extending results by M. Pollicott from the finite to the infinite alphabet se…
Renewal theorems for a class of processes with dependent interarrival times and applications in geometry
Sabrina Kombrink
Renewal theorems are developed for point processes with interarrival times , where is a stochastic process with finite state space…
Lattice-type self-similar sets with pluriphase generators fail to be Minkowski measurable
Sabrina Kombrink, Erin P. J. Pearse, Steffen Winter
A long-standing conjecture of Lapidus claims that under certain conditions, self-similar fractal sets fail to be Minkowski measurable if and only if they are of lattice type. The t…
Minkowski content and fractal Euler characteristic for conformal graph directed systems
Marc Kesseböhmer, Sabrina Kombrink
We study the (local) Minkowski content and the (local) fractal Euler characteristic of limit sets of conformal graph directed systems (cGDS) . For the local…
Minkowski Content and local Minkowski Content for a class of self-conformal sets
Uta Freiberg, Sabrina Kombrink
We investigate (local) Minkowski measurability of images of self-similar sets. We show that (local) Minkowski measurability of a self-similar set implies (lo…
Fractal curvature measures and Minkowski content for one-dimensional self-conformal sets
Marc Kesseböhmer, Sabrina Kombrink
We show that the fractal curvature measures of invariant sets of one-dimensional conformal iterated function systems satisfying the open set condition exist, if and only if the ass…