Gradient variational problems

Richard Kenyon
Yale University
Thursday, October 1, 2020 - 3:30pm to 4:30pm
Zoom ID 91514486597 (contact faculty for pw)

This is joint work with Istvan Prause. Many well-known random tiling models such as domino tilings and square ice lead to variational problems for functions h:R^2->R which minimize a functional depending only on the gradient of h. Other examples of such variational problems include minimal surfaces and surfaces satisfying the "p-laplacian". We give a representation of solutions of such a problem in terms of kappa-harmonic functions: functions which are harmonic for a laplacian with a varying conductance kappa.