Related papers: A vase of catenoids
We derive a minimal generating set of planar moves for diagrams of surfaces embedded in the four-space. These diagrams appear as the bonded classical unlink diagrams.
Piecewise Euclidean structures (identified solid Euclidean polyhedra) on topological 3-dimensional manifolds and pseudo-manifolds are constructed so that they admit pseudo-foliations, a generalized type of foliation. The construction of…
We state several sufficient conditions for compact spacelike surface in the3-dimensional de Sitter space to be totally geodesic or spherical.
We present explicit constructions of orthogonal polynomials inside quadratic bodies of revolution, including cones, hyperboloids, and paraboloids. We also construct orthogonal polynomials on the surface of quadratic surfaces of revolution,…
On objects of a triangulated category with a stability condition, we construct a topology.
Let $\mathcal C$ be a category of a set of (small) categories. This paper concerns with the ${\mathbf {Cat}}$-valued presheaves and sieves over category $\mathcal C.$ Since ${\mathbf {Cat}}$ is not a concrete category, existing definition…
We introduce the notion of a Tits arrangement on a convex open cone as a special case of (infinite) simplicial arrangements. Such an object carries a simplicial structure similar to the geometric representation of Coxeter groups. The…
We prove that a harmonic quasi-isometric map between pinched Hadamard surfaces is a quasi-conformal diffeomorphism.
A condensed set is a sheaf on the site of Stone spaces and continuous maps. We prove that condensed sets are equivalent to sheaves on the site of compact Hausdorff spaces and continuous maps. As an application, we show that there exists a…
In this paper, we consider complete non-catenoidal minimal surfaces of finite total curvature with two ends. A family of such minimal surfaces with least total absolute curvature is given. Moreover, we obtain a uniqueness theorem for this…
We give a comprehensive representation of the construction of dyadic cubes in spaces of homogeneous type.
A ringed finite space is a ringed space whose underlying topological space is finite. The category of ringed finite spaces contains, fully faithfully, the category of finite topological spaces and the category of affine schemes. Any ringed…
There are examples of branched surfaces that do not fully carry laminations, but their preimage in a finite cover does fully carry a lamination
This is an example on the cohomology of threefolds.
We construct free boundary minimal surfaces (FBMS) embedded in the unit ball in the Euclidean three-space which are compact, lie arbitrarily close to the boundary unit sphere, are of genus zero, and their boundary has an arbitrarily large…
In this paper we present a topological way of building a compactification of a symmetric space from a compactification of a Weyl Chamber.
In this note, we construct three new infinite families of surfaces of general type with canonical map of degree 2 onto a surface of general type. For one of these families the canonical system has base points.
We construct sense-preserving univalent harmonic mappings which map the unit disk onto a domain which is convex in the horizontal direction, but with varying dilatation. Also, we obtain minimal surfaces associated with such harmonic…
There are several ways of a construction of a boundary of a symmetric space using pencils of geodesics: the Karpelevich boundary, the visibility boundary, the associahedral boundary, and the sea urchin. We give explicit descriptions of…
A family of algebraic surfaces with many nondegenerate real singularities is introduced with the help of a construction, which has been used in previous works for the generation of substitution tilings.