Discrete conformal variations and discrete scalar curvatures
speaker: David Glickenstein (Department of Mathematics, University of Arizona, Tucson)abstract: Consider a triangulated manifold given a geometry by specifying edge lengths (lengths of 1-simplices) and making the highest dimensional simplices Euclidean. We call these piecewise Euclidean triangulations. It is natural to consider how different angles change if we vary the edge lengths. In this talk, we consider certain variations of length and argue that these are analogous to conformal variations. In particular, in two and three dimensions, there is a close relationship between variations of angle sums and discrete Laplace operators which mimics the relationship of variations of scalar curvature and the Riemannian Laplacian under a conformal variation of Riemannian metrics. This relationship will be made explicit, then we will explore the implications to variations of the discrete Einstein-Hilbert functional (total scalar curvature) as formulated by T. Regge. We will also explore relationships with some previously developed theories of two-dimensional discrete (i.e., piecewise Euclidean) surfaces due to W. Thurston and others.
timetable:
Tue 23 Jun, 9:45 - 10:40, Aula Dini
documents:
Glickenstein
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