3,528 research outputs found
Maximizing Maximal Angles for Plane Straight-Line Graphs
Let be a plane straight-line graph on a finite point set
in general position. The incident angles of a vertex
of are the angles between any two edges of that appear consecutively in
the circular order of the edges incident to .
A plane straight-line graph is called -open if each vertex has an
incident angle of size at least . In this paper we study the following
type of question: What is the maximum angle such that for any finite set
of points in general position we can find a graph from a certain
class of graphs on that is -open? In particular, we consider the
classes of triangulations, spanning trees, and paths on and give tight
bounds in most cases.Comment: 15 pages, 14 figures. Apart of minor corrections, some proofs that
were omitted in the previous version are now include
On the uniqueness of the helicoid and Enneper’s surface in the Lorentz-Minkowski space R31
In this paper we deal with the uniqueness of the Lorentzian helicoid and Enneper’s surface
among properly embedded maximal surfaces with lightlike boundary of mirror symmetry in
the Lorentz-Minkowski space R3Ministerio de Ciencia y TecnologÃa MTM2004-00160Ministerio de Ciencia y TecnologÃa MTM2007-61775Junta de AndalucÃa P06-FQM-01642Junta de AndalucÃa FQM32
Recognizing and Drawing IC-planar Graphs
IC-planar graphs are those graphs that admit a drawing where no two crossed
edges share an end-vertex and each edge is crossed at most once. They are a
proper subfamily of the 1-planar graphs. Given an embedded IC-planar graph
with vertices, we present an -time algorithm that computes a
straight-line drawing of in quadratic area, and an -time algorithm
that computes a straight-line drawing of with right-angle crossings in
exponential area. Both these area requirements are worst-case optimal. We also
show that it is NP-complete to test IC-planarity both in the general case and
in the case in which a rotation system is fixed for the input graph.
Furthermore, we describe a polynomial-time algorithm to test whether a set of
matching edges can be added to a triangulated planar graph such that the
resulting graph is IC-planar
Quasiconvex Programming
We define quasiconvex programming, a form of generalized linear programming
in which one seeks the point minimizing the pointwise maximum of a collection
of quasiconvex functions. We survey algorithms for solving quasiconvex programs
either numerically or via generalizations of the dual simplex method from
linear programming, and describe varied applications of this geometric
optimization technique in meshing, scientific computation, information
visualization, automated algorithm analysis, and robust statistics.Comment: 33 pages, 14 figure
Maximal surfaces in anti-de Sitter 3-manifolds with particles
We prove the existence of a unique maximal surface in each anti-de Sitter
(AdS) convex Globally Hyperbolic Maximal (GHM) manifold with particles (that
is, with conical singularities along time-like lines) for cone angles less than
. We interpret this result in terms of Teichm\"uller theory, and prove the
existence of a unique minimal Lagrangian diffeomorphism isotopic to the
identity between two hyperbolic surfaces with cone singularities when the cone
angles are the same for both surfaces and are less than .Comment: Accepted for publication at "Annales de l'institut Fourier
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