We show that if G is a graph embedded on the projective plane in such a way that each noncontractible cycle intersects G at least n times and the embedding is minimal with respect to this property (i.e., the representativity of the embedding is n), then G can be reduced by a series of reduction oper
Area-minimizing projective planes in 3-manifolds
โ Scribed by H. Bray; S. Brendle; M. Eichmair; A. Neves
- Publisher
- John Wiley and Sons
- Year
- 2010
- Tongue
- English
- Weight
- 112 KB
- Volume
- 63
- Category
- Article
- ISSN
- 0010-3640
No coin nor oath required. For personal study only.
๐ SIMILAR VOLUMES
Let G be a quadrangulation on a surface, and let f be a face bounded by a 4-cycle abcd. A face-contraction of f is to identify a and c (or b and d) to eliminate f . We say that a simple quadrangulation G on the surface is k-minimal if the length of a shortest essential cycle is k(โฅ 3), but any face-
The flag geometry 1=(P, L, I) of a finite projective plane 6 of order s is the generalized hexagon of order (s, 1) obtained from 6 by putting P equal to the set of all flags of 6, by putting L equal to the set of all points and lines of 6, and where I is the natural incidence relation (inverse conta