**Problem of the Week**

**Math Club**

**BUGCAT 2020**

**Zassenhaus Conference**

**Hilton Memorial Lecture**

**BingAWM**

You are here: Homepage » Seminars » Combinatorics Seminar » Ivan Izmestiev (Freie Universität Berlin)

seminars:comb:abstract.201502izm

The discrete Hilbert-Einstein functional (also known as Regge action) for a 3-manifold glued from euclidean simplices is the sum of edge lengths multiplied with angular defects at the edges. There is an analog for hyperbolic cone-manifolds; a discrete total mean curvature term appears if the manifold has a non-empty boundary. Variational properties of this functional are similar to those of its smooth counterpart. In particular, critical points correspond to vanishing angular defects, i.e. to metrics of constant curvature. I survey isometric embeddings and rigidity results that can be obtained by studying the second derivative of the discrete Hilbert-Einstein and speak about possible future developments.

seminars/comb/abstract.201502izm.txt · Last modified: 2020/01/29 14:03 (external edit)

Except where otherwise noted, content on this wiki is licensed under the following license: CC Attribution-Noncommercial-Share Alike 3.0 Unported