3 papers
math.AP2026
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 Gue…
math.NA2025
Computable Poincaré--Friedrichs constants for the de~Rham complex over convex domains and domains with shellable triangulations
Théophile Chaumont-Frelet, Martin Werner Licht, Martin VohralÃk
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…
math.MG2024
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…