6 citations · 13 across the 7 of their papers we have counts for
13 papers
A Sharp Lower Bound for Integral Menger Curvature
Sebastian Scholtes, Alexander Dohmen
We prove that round circles are the unique minimisers of integral Menger curvature among embedded closed curves of prescribed length for every , i.e. $…
Numerics and analysis of Cahn--Hilliard critical points
Tobias Grafke, Sebastian Scholtes, Alfred Wagner +1
We explore recent progress and open questions concerning local minima and saddle points of the Cahn--Hilliard energy in and the critical parameter regime of large system…
Variational Convergence of Discrete Elasticae
Sebastian Scholtes, Henrik Schumacher, Max Wardetzky
We discuss a discretization by polygonal lines of the Euler-Bernoulli bending energy and of Euler elasticae under clamped boundary conditions. We show Hausdorff convergence of the…
Optimal -type relaxation rates for the Cahn-Hilliard equation on the line
Felix Otto, Sebastian Scholtes, Maria G. Westdickenberg
In this paper we derive optimal algebraic-in-time relaxation rates to the kink for the Cahn-Hilliard equation on the line. We assume that the initial data have a finite distance---…
Metastability of the Cahn-Hilliard equation in one space dimension
Sebastian Scholtes, Maria G. Westdickenberg
We establish metastability of the one-dimensional Cahn-Hilliard equation for initial data that is order-one in energy and order-one in away from a point on the so-ca…
Discrete knot energies
Sebastian Scholtes
The present chapter gives an overview on results for discrete knot energies. These discrete energies are designed to make swift numerical computations and thus open the field to co…
Comparing maximal mean values on different scales
Thomas Havenith, Sebastian Scholtes
When computing the average speed of a car over different time periods from given GPS data, it is conventional wisdom that the maximal average speed over all time intervals of fixed…
Discrete Thickness
Sebastian Scholtes
We investigate the relationship between a discrete version of thickness and its smooth counterpart. These discrete energies are defined on equilateral polygons with vertices. I…
Discrete Möbius Energy
Sebastian Scholtes
We investigate a discrete version of the Möbius energy, that is of geometric interest in its own right and is defined on equilateral polygons with segments. We show that the $Γ…
On hypersurfaces of positive reach, alternating Steiner formulae and Hadwiger's Problem
Sebastian Scholtes
We give new characterisations of sets of positive reach and show that a closed hypersurface has positive reach if and only if it is of class . These results are then used…
Tangency properties of sets with finite geometric curvature energies
Sebastian Scholtes
We investigate inverse thickness and the integral Menger curvature energies , and , to find that finite or $\m…
For which positive is the integral Menger curvature finite for all simple polygons?
Sebastian Scholtes
In this brief note we show that the integral Menger curvature is finite for all simple polygons if and only if . For the intermediate energies $\mathc…
A characterisation of inner product spaces by the maximal circumradius of spheres
Sebastian Scholtes
We give a new characterisation of inner product spaces amongst normed vector spaces in terms of the maximal cirumradius of spheres. It turns out that a normed vector space $(X,\nor…