Related papers: A note on minimization of rational surfaces obtain…
By employing the closest point method, we extend the applicability of minimizing movements to the surface PDE setting. The corresponding approximation methods are created, and their convergence is observed. The numerical methods are then…
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 adapt the simulated annealing algorithm to the search of periodic orbits for classical multi-electron atomic systems. This is done by minimizing the n-th return distance to the initial position on a Poincare surface of section under an…
In this paper, we study how to find rational motions that move a line along a given rational ruled surface. Our goal is to find motions with the lowest possible degree using dual quaternions. While similar problems for point trajectories…
The Bj\"orling problem amounts to the construction of a minimal surface from a real-analytic curve with a given real-analytic normal vector field. We approximate that solution locally by discrete minimal surfaces as special discrete…
We introduce a framework for the recovery of points on a smooth surface in high-dimensional space, with application to dynamic imaging. We assume the surface to be the zero-level set of a bandlimited function. We show that the exponential…
We consider reduction of dimension for nonlinear dynamical systems. We demonstrate that in some cases, one can reduce a nonlinear system of equations into a single equation for one of the state variables, and this can be useful for…
We decrease the $rms$ mean curvature and area of a variable surface with a fixed boundary by iterating a few times through a curvature-based variational algorithm. For a boundary with a known minimal surface, starting with a deliberately…
The aim of this paper is to present a construction of smooth rational surfaces in projective fourspace with degree 12 and sectional genus 13. The construction is based on exterior algebra methods, finite field searches and standard…
We suggest a new definition for discrete minimal surfaces in terms of sphere packings with orthogonally intersecting circles. These discrete minimal surfaces can be constructed from Schramm's circle patterns. We present a variational…
In this paper we provide a characterisation of rational developable surfaces in terms of the blossoms of the bounding curves and three rational functions $\Lambda$, $M$, $\nu$. Properties of developable surfaces are revised in this…
We present a practical algorithm to compute models of rational functions with minimal resultant under conjugation by fractional linear transformations. We also report on a search for rational functions of degrees 2 and 3 with rational…
New algorithms are presented for numerical conformal mapping based on rational approximations and the solution of Dirichlet problems by least-squares fitting on the boundary. The methods are targeted at regions with corners, where the…
In this paper we describe an algorithm for implicitizing rational hypersurfaces in case there exists at most a finite number of base points. It is based on a technique exposed in math.AG/0210096, where implicit equations are obtained as…
We study birational morphisms between smooth projective surfaces that respect a given Poisson structure, with particular attention to induced birational maps between the (Poisson) moduli spaces of sheaves on those surfaces. In particular,…
A minimal surface in a random environment (MSRE) is a surface which minimizes the sum of its elastic energy and its environment potential energy, subject to prescribed boundary conditions. Apart from their intrinsic interest, such surfaces…
The goal of this paper is to describe the oscillatory microstructure that can emerge from minimizing sequences for nonconvex energies. We consider integral functionals that are defined on real valued (scalar) functions $u(x)$ which are…
The rapidly evolving field of engineering design of functional surfaces necessitates sophisticated tools to manage the inherent complexity of high-dimensional design spaces. This survey paper offers a scoping review, i.e., a literature…
We introduce a sampling theoretic framework for the recovery of smooth surfaces and functions living on smooth surfaces from few samples. The proposed approach can be thought of as a nonlinear generalization of union of subspace models…
In this paper, we study how the degrees of the elements in a minimal $\mu$-basis of a parametrized surface behave. For an arbitrary rational surface parametrization $P(s,t)=(a_1(s,t),a_2(s,t),a_3(s,t),a_4(s,t)) \in \mathbb{F}[s,t]^4$ over…