6,938 research outputs found
Steiner Variations on Random Surfaces
Ambartzumian et.al. suggested that the modified Steiner action functional had
desirable properties for a random surface action. However, Durhuus and Jonsson
pointed out that such an action led to an ill-defined grand-canonical partition
function and suggested that the addition of an area term might improve matters.
In this paper we investigate this and other related actions numerically for
dynamically triangulated random surfaces and compare the results with the
gaussian plus extrinsic curvature actions that have been used previously.Comment: 8 page
Calabi-Yau Threefolds Fibred by Mirror Quartic K3 Surfaces
We study threefolds fibred by mirror quartic K3 surfaces. We begin by showing
that any family of such K3 surfaces is completely determined by a map from the
base of the family to the moduli space of mirror quartic K3 surfaces. This is
then used to give a complete explicit description of all Calabi-Yau threefolds
fibred by mirror quartic K3 surfaces. We conclude by studying the properties of
such Calabi-Yau threefolds, including their Hodge numbers and deformation
theory.Comment: v2: Significant changes at the request of the referee. Section 3 has
been rearranged to accommodate a revised proof of Proposition 3.5 (formerly
3.2). Section 5 has been removed completely, it will instead appear as part
of Section 5 in arxiv:1601.0811
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Uniform subdivision algorithms for curves and surfaces
A convergence analysis for studying the continuity and differentiability of limit curves generated by uniform subdivision algorithms is presented. The analysis is based on the study of corresponding difference and divided difference algorithms. The alternative process of "integrating" the algorithms is considered. A specific example of a 4-point interpolatory curve algorithm is described and its generalization to a surface algorithm defined over a subdivision of a regular triangular partition is illustrated
Digraphs and cycle polynomials for free-by-cyclic groups
Let \phi \in \mbox{Out}(F_n) be a free group outer automorphism that can be
represented by an expanding, irreducible train-track map. The automorphism
determines a free-by-cyclic group
and a homomorphism . By work of Neumann,
Bieri-Neumann-Strebel and Dowdall-Kapovich-Leininger, has an open cone
neighborhood in whose integral points
correspond to other fibrations of whose associated outer automorphisms
are themselves representable by expanding irreducible train-track maps. In this
paper, we define an analog of McMullen's Teichm\"uller polynomial that computes
the dilatations of all outer automorphism in .Comment: 41 pages, 20 figure
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