Related papers: Local interpolation for minimal surfaces
We study the approximation of maps into complex manifolds along with interpolation on certain compact subsets of the plane. Results are also obtained regarding approximation and interpolation of sections of holomorphic submersions.
Given a smooth, irreducible, projective surface $S$, let $g(S)$ be the minimum geometric genus of an irreducible curve that moves in a linear system of positive dimension on $S$. We determine the value of this birational invariant for a…
In this paper we consider a three dimensional Kropina space and obtain the partial differential equation that characterizes a minimal surfaces with the induced metric. Using this characterization equation we study various immersions of…
We show that immersed minimal surfaces of $\mathbb{R}^{3}$ with bounded curvature and proper self intersections are proper. We also show that the restriction of the immersing map to a wide component is always proper. When the immersing map…
In the paper, the planar polynomial geometric interpolation of data points is revisited. Simple sufficient geometric conditions that imply the existence of the interpolant are derived in general. They require data points to be convex in a…
Algebraic curve interpolation is described by specifying the location of N points in the plane and constructing an algebraic curve of a function f that should pass through them. In this paper, we propose a novel approach to construct the…
We consider a real interpolation method defined by means of slowly varying functions. We present some reiteration formulae including so called $L$ or $R$ limiting interpolation spaces. These spaces arise naturally in reiteration formulae…
We consider real forms of relatively minimal rational surfaces F_m. Connected components of moduli of real non-singular curves in |-2K_{F_m}| had been classified recently for m=0, 1, 4 in math.AG/0312396. Applying similar methods, here we…
We are interested in the algebraic intersection of closed curves of a given length on translation surfaces. Namely, we study the quantity KVol which measures how many times can two closed curves of a given length intersect. In this paper,…
This short article, which appeared in the MSRI Fall 2004 newletter, is intended for a general mathematical audience. It describes some mathematical themes from the Winter 2004 program at MSRI in topological aspects of real algebraic…
We show that the image of a nonconstant conformal harmonic map $\mathbb C\to \mathbb R^3$, not necessarily proper and possibly with branch points, intersects every properly embedded nonflat minimal surface of bounded curvature in $\mathbb…
The paper gives topological as well as rigid isotopy classification of smooth irreducible algebraic curves in the real projective 3-space for the case when the degree of the curve is at most six and its genus is at most one.
We study the structure of collections of algebraic curves in three dimensions that have many curve-curve incidences. In particular, let $k$ be a field and let $\mathcal{L}$ be a collection of $n$ space curves in $k^3$, with…
Graph-based approximation methods are of growing interest in many areas, including transportation, biological and chemical networks, financial models, image processing, network flows, and more. In these applications, often a basis for the…
We investigate minimal surfaces passing a given curve in $R^{3}$. Using the Frenet frame of a given curve and isothermal parameter, we derive the necessary and sufficient condition for minimal surface. Also we derive the parametric…
The purpose of this article is to introduce a new class of kernels on SO(3) for approximation and interpolation, and to estimate the approximation power of the associated spaces. The kernels we consider arise as linear combinations of…
We show that in a closed 3-manifold with a generic metric of positive Ricci curvature, there are minimal surfaces of arbitrary large Morse index, which partially confirms a conjecture by F. Marques and A. Neves. We prove this by analyzing…
In this paper, we study $\mathbb{A}^1$ curves on log K3 surfaces. We classify all genuine log K3 surfaces of type II which admits countably infinite $\mathbb{A}^1$ curves.
This paper gives a general interpretation of Linear Prediction (LP) by interpolation framework different from the perspective of statistics. This interpretation is proved to be useful by several following results, such as: The mechanism of…
Extending Culler-Shalen theory, Hara and the second author presented a way to construct certain kinds of branched surfaces in a $3$-manifold from an ideal point of a curve in the $\operatorname{SL}_n$-character variety. There exists an…