Remote Access Conformal Geometry and Dynamics
Green Open Access

Conformal Geometry and Dynamics

ISSN 1088-4173



Bounded outdegree and extremal length on discrete Riemann surfaces

Author: William E. Wood
Journal: Conform. Geom. Dyn. 14 (2010), 194-201
MSC (2000): Primary 52C26; Secondary 53A30, 05C10, 57M15
Published electronically: August 2, 2010
MathSciNet review: 2672225
Full-text PDF Free Access

Abstract | References | Similar Articles | Additional Information

Abstract: Let $T$ be a triangulation of a Riemann surface. We show that the $1$-skeleton of $T$ may be oriented so that there is a global bound on the outdegree of the vertices. Our application is to construct extremal metrics on triangulations formed from $T$ by attaching new edges and vertices and subdividing its faces. Such refinements provide a mechanism of convergence of the discrete triangulation to the classical surface. We will prove a bound on the distortion of the discrete extremal lengths of path families on $T$ under the refinement process. Our bound will depend only on the refinement and not on $T$. In particular, the result does not require bounded degree.

References [Enhancements On Off] (What's this?)


Similar Articles

Retrieve articles in Conformal Geometry and Dynamics of the American Mathematical Society with MSC (2000): 52C26, 53A30, 05C10, 57M15

Retrieve articles in all journals with MSC (2000): 52C26, 53A30, 05C10, 57M15

Additional Information

William E. Wood
Affiliation: Department of Mathematics and Computer Science, 1600 Washington Avenue, Hendrix College, Conway, Arkansas 72032

Keywords: Discrete conformal geometry, extremal length
Received by editor(s): September 1, 2009
Published electronically: August 2, 2010
Article copyright: © Copyright 2010 American Mathematical Society
The copyright for this article reverts to public domain 28 years after publication.