Speaker
Evan Gawlik
(Santa Clara University)
Description
If a simplicial triangulation is equipped with a piecewise smooth Riemannian metric that has single-valued tangential-tangential components on element interfaces, then there are various notions of curvature that one can define, even though the classical formulas for curvature involving derivatives of the metric no longer make sense. In this talk, I will explain the origins of these definitions and summarize what is known about the convergence of these discrete curvatures under refinement of the triangulation. The curvatures that I will discuss include the scalar curvature, Einstein curvature tensor, and Riemann curvature tensor. This is joint work with Yakov Berchenko-Kogan and Michael Neunteufel.
Authors
Yakov Berchenko-Kogan
(Florida Institute of Technology)
Evan Gawlik
(Santa Clara University)
Dr
Michael Neunteufel
(TU Wien)