30 citations · 376 across the 49 of their papers we have counts for
5 papers · 1 filter
Quenching for a semi-linear wave equation for MEMS
Heiko Gimperlein, Runan He, Andrew A. Lacey
We consider the formation of finite-time quenching singularities for solutions of semi-linear wave equations with negative power nonlinearities, as can model micro-electro-mechanic…
Poisson transform and unipotent complex geometry
Heiko Gimperlein, Bernhard Krötz, Luz Roncal +1
Our concern is with Riemannian symmetric spaces of the non-compact type and more precisely with the Poisson transform which maps generalized functions on th…
Efficient quantitative assessment of robot swarms: coverage and targeting Lévy strategies
Siobhan Duncan, Gissell Estrada-Rodriguez, Jakub Stocek +3
Biologically inspired strategies have long been adapted to swarm robotic systems, including biased random walks, reaction to chemotactic cues and long-range coordination. In this p…
The magnitude and spectral geometry
Heiko Gimperlein, Magnus Goffeng, Nikoletta Louca
We study the geometric significance of Leinster's notion of magnitude for a smooth manifold with boundary of arbitrary dimension, motivated by open questions for the unit disk in $…
Semiclassical analysis of a nonlocal boundary value problem related to magnitude
Heiko Gimperlein, Magnus Goffeng, Nikoletta Louca
We study a Dirichlet boundary problem related to the fractional Laplacian in a manifold. Its variational formulation arises in the study of magnitude, an invariant of compact metri…