Related papers: Patches of developable surfaces bounded by NURBS c…
This paper presents a new method for modelling the dynamic behaviour of developable ribbons, two dimensional strips with much smaller width than length. Instead of approximating such surface with a general triangle mesh, we characterize it…
We apply a variant of the square-sieve to produce a uniform upper bound for the number of rational points of bounded height on a family of surfaces that admit a fibration over the projective line, whose general fibre is a hyperelliptic…
This paper presents the development of a complete CAD-compatible framework for structural shape optimization in 3D. The boundaries of the domain are described using NURBS while the interior is discretized with B\'ezier tetrahedra. The…
PhD dissertation consists in three lines of investigation involving rational elliptic surfaces, namely 1) a study of conic bundles on these surfaces; 2) an investigation of the possible intersection numbers of two sections and 3) a theorem…
We argue that for a smooth surface S, considered as a ramified cover over the projective plane branched over a nodal-cuspidal curve B one could use the structure of the fundamental group of the complement of the branch curve to understand…
We study the set of rational curves of a certain topological type in general members of certain families of Calabi-Yau threefolds. For some families we investigate to what extent it is possible to conclude that this set is finite. For other…
We initiate the study of computing shortest non-separating simple closed curves with some given topological properties on non-orientable surfaces. While, for orientable surfaces, any two non-separating simple closed curves are related by a…
Given a smooth cubic hypersurface $X$ over a finite field of characteristic greater than 3 and two generic points on $X$, we use a function field analogue of the Hardy-Littlewood circle method to obtain an asymptotic formula for the number…
We study degree two unirational parameterizations of geometrically rational surfaces over the real field.
We classify incompressible, boundary-incompressible, nonorientable surfaces in punctured-torus bundles over $S^1$. We use the ideas of Floyd, Hatcher, and Thurston. The main tool is to put our surface in the "Morse position" with respect to…
Multi-sided surfaces are often defined by side interpolants (also called ribbons), i.e. the surface has to connect to the ribbons with a prescribed degree of smoothness. The I-patch is such a family of implicit surfaces capable of…
We use admissible covers to characterize irreducible stable curves that are $(d,h)$-elliptic, that is, that are limits of smooth curves admiting finite maps of degree-$d$ to smooth curves of genus $h\geq 1$.
We analyze morphisms from pointed curves to K3 surfaces with a distinguished rational curve, such that the marked points are taken to the rational curve, perhaps with specified cross ratios. This builds on work of Mukai and others…
We construct isoperimetric regions from separating hypersurfaces in closed manifolds. This yields isoperimetric boundaries exhibiting a wide variety of topological types and singular sets.
We construct infinitesimal deformations on an open domain of a smooth projective surface given by a complement of plumbings of disjoint linear chains of smooth rational curves. We show that the infinitesimal deformations are not small…
In this paper, we construct geometrically finite rational maps with buried critical points on the boundaries of some hyperbolic components by using the pinching and plumbing deformations.
We use twisted stable maps to compute the number of rational degree d plane curves having prescribed contacts to a smooth plane cubic.
In this paper, we study Mannheim surface offsets in dual space. By the aid of the E. Study Mapping, we consider ruled surfaces as dual unit spherical curves and define the Mannheim offsets of the ruled surfaces by means of dual geodesic…
For a class of compactly supported windows we characterize the frame property for a Gabor system $\mts,$ for translation parameters $a$ belonging to a certain range depending on the support size. We show that the obstructions to the frame…
We study the family of rational curves on arbitrary smooth hypersurfaces of low degree using tools from analytic number theory.