23 citations · 51 across the 10 of their papers we have counts for
11 papers
Torsional rigidity and isospectral planar sets
Joseph Comer, Patrick McDonald
We prove that a certain pair of isospectral planar sets are distinguished by torsional rigidity.
Extremizing Temperature Functions of Rods with Robin Boundary Conditions
Jeffrey J. Langford, Patrick McDonald
We compare the solutions of two one-dimensional Poisson problems on an interval with Robin boundary conditions, one with given data, and one where the data has been symmetrized. Wh…
Comparison Results, Exit Time Moments, And Eigenvalues On Riemannian Manifolds With A Lower Ricci Curvature Bound
Don Colladay, Jeffrey J. Langford, Patrick McDonald
We study the relationship between the geometry of smoothly bounded domains in complete Riemannian manifolds and the associated sequence of -norms of exit time moments for Brow…
Exit Time Moments and Eigenvalue Estimates
Emily B. Dryden, Jeffrey J. Langford, Patrick McDonald
We study estimates involving the principal Dirichlet eigenvalue associated to a smoothly bounded domain in a complete Riemannian manifold and L1-norms of exit time moments of Brown…
Torsional Rigidity, Isospectrality and Quantum Graphs
Don Colladay, Leon Kaganovskiy, Patrick McDonald
We study torsional rigidity for graph and quantum graph analogs of well-known pairs of isospectral non-isometric planar domains. We prove that such isospectral pairs are distinguis…
Heat content determines planar triangles
Reed Meyerson, Patrick McDonald
We prove that heat content determines planar triangles.