Emil Saucan
Biographic Data
| ID | 4164007 |
|---|---|
| NAME | Emil Saucan |
| GIVEN NAMES | Emil |
| FAMILY NAME | Saucan |
| SIGNATURE | SAUCAN E |
| AFFILIATIONS | Max Planck Institute for Mathematics |
| ORCID | 0000-0001-9033-0828 |
| VERIFIED | Yes |
| TOTAL WORKS | 2 |
| TOTAL CITATIONS | 0 |
| WORKS AS AUTHOR | 2 |
| WORKS AS EDITOR | 0 |
| FIRST PUBLICATION YEAR | 2011 |
| LATEST PUBLICATION YEAR | 2020 |
| H-INDEX | 0 |
A simple differential geometry for complex networks
We introduce new definitions of sectional, Ricci, and scalar curvatures for networks and their higher dimensional counterparts, derived from two classical notions of curvature for curves in general metric spaces, namely, the Menger curvature and the Haantjes curvature. These curvatures are applicable to unweighted or weighted and undirected or directed networks and are more intuitive and easier to compute than other network curvatures. In particu…
Curvature based triangulation of metric measure spaces
We prove that a Ricci curvature based method of triangulation of compact Riemannian manifolds, due to Grove and Petersen, extends to the context of weighted Riemannian manifolds and more general metric measure spaces. In both cases the role of the lower bound on Ricci curvature is replaced by the curvature-dimension condition ${\rm CD}(K,N)$. We show also that for weighted Riemannian manifolds the triangulation can be improved to become a thick o…
No prominent works on this page.
Curvature based triangulation of metric measure spaces
We prove that a Ricci curvature based method of triangulation of compact Riemannian manifolds, due to Grove and Petersen, extends to the context of weighted Riemannian manifolds and more general metric measure spaces. In both cases the role of the lower bound on Ricci curvature is replaced by the curvature-dimension condition ${\rm CD}(K,N)$. We show also that for weighted Riemannian manifolds the triangulation can be improved to become a thick o…
A simple differential geometry for complex networks
We introduce new definitions of sectional, Ricci, and scalar curvatures for networks and their higher dimensional counterparts, derived from two classical notions of curvature for curves in general metric spaces, namely, the Menger curvature and the Haantjes curvature. These curvatures are applicable to unweighted or weighted and undirected or directed networks and are more intuitive and easier to compute than other network curvatures. In particu…
Computer Science (2 works) · Curvature (2 works) · Geometric Analysis and Curvature Flows (2 works) · Geometry (2 works) · Mathematics (2 works) · Pure mathematics (2 works) · Ricci curvature (2 works) · Scalar curvature (2 works) · Sectional curvature (2 works) · Topological and Geometric Data Analysis (2 works)