Related papers: A note on minimization of rational surfaces obtain…
We construct closed embedded minimal surfaces in the round three-sphere, resembling two parallel copies of the equatorial two-sphere, joined by small catenoidal bridges symmetrically arranged either along two parallel circles of the…
In the literature on X-ray transform and Transport Twistor (TT) spaces, blow-down maps (or maps with holomorphic blow-down structure as defined in [BMP24]) are maps that desingularize the degenerate complex structure of the TT space of an…
We construct a linearly normal smooth rational surface S of degree 11 and sectional genus 8 in the projective fivespace. Surfaces satisfying these numerical invariants are special, in the sense that $h^1(\mathscr{O}_S(1))>0$. Our…
The reduction of dynamical systems has a rich history, with many important applications related to stability, control and verification. Reduction of nonlinear systems is typically performed in an exact manner - as is the case with…
We review and compare different computational variational methods applied to a system of fourth order equations that arises as a model of cylinder buckling. We describe both the discretization and implementation, in particular how to deal…
We consider model order reduction of parameterized Hamiltonian systems describing nondissipative phenomena, like wave-type and transport dominated problems. The development of reduced basis methods for such models is challenged by two main…
We introduce a novel and powerful method for exploring the properties of the multidimensional free energy surfaces of complex many-body systems by means of a coarse-grained non-Markovian dynamics in the space defined by a few collective…
Harmonic mappings have long intrigued researchers due to their intrinsic connection with minimal surfaces. In this paper, we investigate shearing of two distinct classes of univalent conformal mappings which are convex in horizontal…
We study the algebraic dynamical systems generated by triangular systems of rational functions and estimate the height growth of iterations generated by such systems. Further, using a result on the reduction modulo primes of systems of…
We study the birational properties of geometrically rational surfaces from a derived categorical point of view. In particular, we give a criterion for the rationality of a del Pezzo surface over an arbitrary field, namely, that its derived…
Using orbifold Hilbert schemes, we compactify all two-dimensional Hitchin systems corresponding to types A0-tilde, D4-tilde, E6-tilde, E7-tilde, and E8-tilde, thereby obtaining four rational elliptic surfaces with C*-actions. Their singular…
When a material surface is functionalized so as to acquire some type of order, functionalization of which soft condensed matter systems have recently provided many interesting examples, the modeller faces an alternative. Either the order is…
This paper further studies the matroid realization space of a specific deformation of the regular $n$-gon with its lines of symmetry. Recently, we obtained that these particular realization spaces are birational to the elliptic modular…
Within the framework of linear-scaling Kohn-Sham density functional theory, a robust method for maintaining compact localized orbitals close to the ground state is coupled with nuclear dynamics. This allows to obviate the commonly employed…
A minimal surface in a random environment (MSRE) is a $d$-dimensional surface in $(d+n)$-dimensional space which minimizes the sum of its elastic energy and its environment potential energy, subject to prescribed boundary values. Apart from…
This paper proposes a simple technique of curve and surface construction with B-splines. Given a control polygon or a control mesh together with node ordinates corresponding to all control points, a rational curve or surface is obtained by…
In this paper, we discuss the minimal surfaces over the slanted half-planes, vertical strips, and single slit whose slit lies on the negative real axis. The representation of these minimal surfaces and the corresponding harmonic mappings…
The conformal structure on minimal surfaces plays a key role in studying the properties of minimal surfaces. Here we extend the results of uniformization of surfaces with boundary to get the (weak) uniformization results for triple junction…
In this paper we propose an elementary topological approach which unifies and extends various different results concerning fixed points and periodic points for maps defined on sets homeomorphic to rectangles embedded in euclidean spaces. We…
We calculate the minimal surface bounded by four-sided figures whose projection on a plane is a rectangle, starting with the bilinear interpolation and using, for smoothness, the Chebyshev polynomial expansion in our discretized numerical…