Related papers: Logarithmically spiraling helicoids
Given a tiling $\mathcal{T}$ of the plane by straight edge polygons, which is invariant by two independent translations, we construct a family of embedded triply periodic minimal surfaces which desingularizes $\mathcal{T}\times\mathbb{R}$.…
The purpose of this paper is to study singular holomorphic foliations of arbitrary codimension defined by logarithmic forms on projective spaces.
We consider the question of existence of embedded doubly periodic minimal surfaces in Euclidean 3-space with Scherk-type ends, surfaces that topologically are Scherk's doubly periodic surface with handles added in various ways. We extend…
We study the local analytic classification of affine structures with logarithmic pole on complex surfaces. With this result in hand, we can get the local classification of the logarithmic parallelizable d-webs, d $\ge$ 3.
We consider skew ruled surfaces in the three-dimensional Euclidean space and some geometrically distinguished families of curves on them whose normal curvature has a concrete form. The aim of this paper is to find and classify all ruled…
This survey focuses on the geometric problem of log-surfaces, which are pairs consisting of a smooth projective surface and a reduced non-empty boundary divisor. In the first part, we focus on the geography problem for complex log-surfaces…
This paper characterizes a compact piece of the helicoid $H_C$ in a solid cylinder $C \subset \mathbb{R}^3$ from the following two perspectives. First, under reasonable conditions, $H_C$ has the smallest area among all immersed surfaces…
We construct knotted proper holomorphic embeddings of the unit disc in C^2.
We construct a complete, embedded minimal surface in euclidean 3-space which has unbounded Gaussian curvature. It has infinite genus, infinitely many catenoidal type ends and one limit end.
We produce examples of complex algebraic surfaces with isolated singularities such that these singularities are not metrically conic, i.e. the germs of the surfaces near singular points are not bi-Lipschitz equivalent, with respect to the…
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 describe a new deformation that connects minimal disks with planar ends with minimal disks with helicoidal ends. In this way, we are able to construct a family of complete minimal surfaces with helicoidal ends that contains…
In this paper we survey with complete proofs some well--known, but hard to find, results about constructing closed embedded minimal surfaces in a closed 3-dimensional manifold via min--max arguments. This includes results of J. Pitts, F.…
We investigate a quantization problem which asks for the construction of an algebra for relative elliptic problems of pseudodifferential type associated to smooth embeddings. Specifically, we study the problem for embeddings in the category…
We show that there exists a metric with positive scalar curvature on S2xS1 and a sequence of embedded minimal cylinders that converges to a minimal lamination that, in a neighborhood of a strictly stable 2-sphere, is smooth except at two…
We introduce the class of rational plane curves parameterizable by conics as an extension of the family of curves parameterizable by lines (also known as monoid curves). We show that they are the image of monoid curves via suitable…
In this article we introduce a notion of logarithmic co-Higgs sheaves associated to a simple normal crossing divisor on a projective manifold, and show their existence with nilpotent co-Higgs fields for fixed ranks and second Chern classes.…
Sub-micro structured surfaces allow modifying the behavior of polymer films or components. Especially in micro fluidics a lotus-like characteristic is requested for many applications. Structure details with a high aspect ratio are necessary…
We study properly embedded and immersed p(pseudohermitian)-minimal surfaces in the 3-dimensional Heisenberg group. From the recent work of Cheng, Hwang, Malchiodi, and Yang, we learn that such surfaces must be ruled surfaces. There are two…
In this note we present a computational approach to the construction of ovoids of the Hermitian surface and show some related experimental results.