4 papers
Eigenvalue growth of the discrete Hodge Laplacian across dimensions
Philipp Bartmann, Matthias Keller
We prove several bounds on the largest and smallest eigenvalues of the combinatorial Hodge Laplacian of a finite simplicial complex As a consequence, we obtain new van…
The complex property of the boundary operator on simplicial complexes
Philipp Bartmann, Matthias Keller
We study the complex property of the boundary operator on a weighted, infinite, and possibly non-locally finite simplicial complex. We give a char…
The heat equation and independence of the spectrum of the Hodge Laplacian on
Philipp Bartmann, Matthias Keller
We study the heat equation associated to the Hodge Laplacian on simplicial complexes. Using recently developed techniques for magnetic Schrödinger operators, we prove Davies-Gaffn…
On Hodge Laplacians on General Simplicial Complexes
Philipp Bartmann, Matthias Keller
We study Laplacians on general countable weighted simplicial complexes from a conceptual point of view. These operators will first be introduced formally before showing that those…