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math.DG2024
Riesz energies and the magnitude of manifolds
Heiko Gimperlein, Magnus Goffeng
We study the geometric significance of Leinster's magnitude invariant. For closed manifolds we find a precise relation with Brylinski's beta function and therefore with classical i…
math.DG2022
Index theory of hypoelliptic operators on Carnot manifolds
Magnus Goffeng, Alexey Kuzmin
We study the index theory of hypoelliptic operators on Carnot manifolds -- manifolds whose Lie algebra of vector fields is equipped with a filtration induced from sub-bundles of th…
math.DG2022★ 1 cited
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 $…