9 citations · 18 across the 7 of their papers we have counts for
10 papers
Cheeger constants of hyperbolic reflection groups and Maass cusp forms of small eigenvalues
Brian A. Benson, Grant S. Lakeland, Holger Then
We compute the Cheeger constants of a collection of hyperbolic surfaces corresponding to maximal non-compact arithmetic Fuchsian groups, and to subgroups which are the rotation sub…
Volume growth, curvature, and Buser-type inequalities in graphs
Brian Benson, Peter Ralli, Prasad Tetali
We study the volume growth of metric balls as a function of the radius in discrete spaces, and focus on the relationship between volume growth and discrete curvature. We improve vo…
Mean Value Theorems for Riemannian Manifolds via the Obstacle Problem
Brian Benson, Ivan Blank, Jeremy LeCrone
We develop some of the basic theory for the obstacle problem on Riemannian Manifolds, and we use it to establish a mean value theorem. Our mean value theorem works for a very wide…
The Cheeger Constant, Isoperimetric Problems, and Hyperbolic Surfaces
Brian Benson
We give a brief literature review of the isoperimetric problem and discuss its relationship with the Cheeger constant of Riemannian -manifolds. For some non-compact, finite area…
Torsion and ground state maxima: close but not the same
Brian A. Benson, Richard S. Laugesen, Michael Minion +1
Could the location of the maximum point for a positive solution of a semilinear Poisson equation on a convex domain be independent of the form of the nonlinearity? Cima and Derrick…
Sturm-Liouville Estimates for the Spectrum and Cheeger Constant
Brian Benson
Buser's inequality gives an upper bound on the first non-zero eigenvalue of the Laplacian of a closed manifold M in terms of the Cheeger constant h(M). Agol later gave a quantitati…