Geometric triangulations and discrete Laplacians on manifolds

By David Glickenstein. 2005

69 citations recorded by the source corpus.

This paper uses the technology of weighted and regular triangulations to study discrete versions of the Laplacian on piecewise Euclidean manifolds. Regular triangulations are studied in some detail, including flip algorithms. The Laplacian is then studied as an operator on functions of the vertices as a generalized weighted Laplacian on graphs.

Subfields: Applied Mathematics, Computational Theory and Mathematics, Geometry and Topology

View Paper: https://www.semanticscholar.org/paper/7d8b344838de1280e8a82c74189fbc895fb45dc5

How researchers see this paper

The researchers whose trusted networks rank it highest, strongest advocate first. Every researcher gets a different order.

In Applied Mathematics

1. Alexander I. Bobenko
2. Ivan Izmestiev
3. David Glickenstein
4. Xu Xu
5. Feng Luo
6. Huabin Ge
7. Ren Guo

In Computational Theory and Mathematics

1. David Glickenstein
2. Alexander I. Bobenko
3. Ivan Izmestiev
4. Huabin Ge
5. Feng Luo
6. Xu Xu

In Geometry and Topology

1. David Glickenstein
2. Alexander I. Bobenko
3. Ivan Izmestiev
4. Feng Luo
5. Boris A. Springborn
6. Huabin Ge
7. Xu Xu

Citations in the corpus

• ALEXANDROV'S THEOREM, WEIGHTED DELAUNAY TRIANGULATIONS, AND MIXED VOLUMES (2006, background): “ and M the convex hull of V , see [4], [9], [13]. It can be shown that in this case Definition 2.3 is equivalent to the classical one. Weighted Delaunay triangulations of polyhedral surfaces appear in [14], [21]. However, Definition 2.3 seems to be new. 14 Theorem 2 If M is the sphere and V = Σ, then ”
• Discrete conformal variations and scalar curvature on piecewise flat two and three dimensional manifolds (2009, background): “…of angles in a three-dimensional piecewise flat manifold under conformal variations, and the space of conformal variations is quite large and need not depend on the initial distribution of the edge lengths (unlike [17], where one must assume that the metric comes form a sphere packing…”