4 papers
On solid angles and simplex shape measures
Martin W. Licht
The minimum solid angle of a simplex is shown to be a shape measure in any dimension. While this has been known in dimensions two and three, the higher-dimensional generalization i…
Computable Poincaré--Friedrichs constants for the de~Rham complex over convex domains and domains with shellable triangulations
Théophile Chaumont-Frelet, Martin Werner Licht, Martin Vohralík
We construct potentials for the exterior derivative, in particular, for the gradient, the curl, and the divergence operators, over domains with shellable triangulations. Notably, t…
On the geometry of star domains and the spectra of Hodge-Laplace operators
Martin Werner Licht
We study Poincaré--Friedrichs--Weber constants for Sobolev differential forms on bounded convex domains and on domains star-shaped with respect to a ball. Generalizing work by Guer…
On Lipschitz partitions of unity and the Assouad--Nagata dimension
Martin W. Licht
We show that the standard partition of unity subordinate to an open cover of a metric space has Lipschitz constant , where is the Lebesgue nu…