My broad research interests include topics in geometric analysis, differential geometry, PDE, low dimensional topology, and graph theory. For specific information about details of and motivation for my work, please see the following research overview. Thank you for your interest!
A research colloquium talk I gave to a general mathematics audience at California State University-San Bernardino.
Published and Accepted for Publication
Mean Value Theorems for Riemannian Manifolds via the Obstacle Problem. Joint with Ivan Blank and Jeremy LeCrone. Journal of Geometric Analysis, Vol 29, Issue 3, 2752-2775, DOI:10.1007/s12220-018-0093-4, arXiv:1704.07518.
A note on a Newtonian Approximation in a Schwarzchild background. Joint with Marcelo M. Disconzi. The African Review of Physics, Vol 13, 2018, 12 pages.
Torsion and ground state maxima: close but not the same. Joint with Richard S. Laugesen, Michael L. Minion, and Bartlomiej A. Siudeja. Irish Mathematical Society Bulletin 78 (Winter 2016) 81-88, arXiv:1507.01565.
Preprints and Works Submitted for Peer-Review
The Cheeger Constant, Isoperimetric Problems, and Hyperbolic Surfaces. arXiv:1509.08993
Work in Progress
Cheeger Constants of Principal Congruence Arithmetic Surfaces. Joint with Jeffrey Meyer