arXiv research

Paper proves uniqueness of catenary cylinders based on their asymptotic shape.

The paper proves cylindrical nature of singular minimal ruled surfaces.

In this paper, we consider the problem of finding the hypersurface M^n in the Euclidean (n+1)-space R^{n+1} that satisfies an equation of mean curvature type, called singular minimal hypersurface equation. Such an equation physically characterizes the hypersurfaces in the upper halfspace (R^{n+1})_{+} with lowest gravi…

Catenaries defined on any Riemannian surface using intrinsic distance.

Study stability and bifurcation of liquid interfaces in cylindrical supports.

The study defines and characterizes extrinsic catenaries in hyperbolic space.

The paper studies dual catenaries in the dual plane, deriving equations and characterizations.

The paper defines catenary curves in spheres and hyperbolic planes.

The paper studies hanging chains and surfaces in degenerate geometries.

In this paper we generalize in Lorentz-Minkowski space $ł^3$ the two-dimensional analogue of the catenary of Euclidean space. We solve the Dirichlet problem for bounded mean convex domains and spacelike boundary data that have a spacelike extension to the domain. We also classify all singular maximal surfaces of $ł^3$ …

We consider an appoximation of a catenoid constructed from "odd" truncated cones that maintains minimality in a certain sense. Thorough this procedure, we obtain a discrete curve approximating a catenary by exploiting the fact that it is the function that generates a catenoid. In this investigation, the theory of the G…

Characterizes curves for minimal surfaces in de Sitter space.

We define cylinder knots as billiard knots in a cylinder. We present a necessary condition for cylinder knots: after dividing cylinder knots by possible rotational symmetries we obtain ribbon knots. We obtain an upper bound for the number of cylinder knots with two fixed parameters (out of three). In addition we prove …

Minimal cylinders in Heisenberg group characterized using loop group method.

Holomorphic cylinders converge to disks joined by flow lines.

Two ancient solutions to Gauss curvature flow are identified for cylinders.

The paper develops a method to map knots in a cylinder to virtual-flat knots.

In this paper we show how the existence of a certain stable cylinder determines (locally) the ambient manifold where it is immersed. This cylinder has to verify a {\it bifurcation phenomena}, we make this explicit in the introduction. In particular, the existence of such a stable cylinder implies that the ambient manif…

Cylinders in warped product spaces have zero curvature.

We establish a vanishing result for the $L_{q,p}$-cohomology ($q\ge p$) of a twisted cylinder, which is a generalization of a warped cylinder. The result is new even for warped cylinders. We base on the methods for proving the $(p,q)$ Sobolev--Poincaré inequality developed by L.~Shartser.

The paper examines the stability of Killing cylinders in hyperbolic space.

Knots parametrized in cylinder coordinates by t -> (st, 3 + cos(nt), cos(mt + φ)) share properties of Lissajous and billiard knots in a cylinder. We use these 'billiard knots in a flat solid torus' to study two topics: when is Z(s,n,m) equal to Z(s,m,n)? And: why are the determinants of certain Lissajous and billiard k…

This paper explores how pairs of multicurves can be realized as cylinders on translation surfaces.

Study decomposes geometric surfaces, finding special curves.

New findings on $κ$-solutions with round cylinder as asymptotic shrinker.

Round cylinders are rigid in Ricci shrinkers close to the standard product.

Stable cylinders found in hyperbolic groups and curve graphs.

Study on quantum particle evolution on Grushin cylinder, embedding in R^3.

We consider cylinders in ${\cal H}^2\times R$ (see definitions in the introduction) and prove that a complete and connected surface in ${\cal H}^2\times R$ with the vanishing of the Gauss and extrinsic curvatures is a cylinder.

In 1991, Dajczer and Rodriguez proved in [10] that a complete minimal real Kahler submanifold of codimension 2, if with complex dimension > 2, would be either holomorphic, or a cylinder, or complex ruled. In this article, we generalize their result to real analytic complete real Kahler submanifolds of codimension 4. Th…

Study constructs closed curves with constant curvature on cylinders and tori.

Study proves uniqueness and rigidity of cylindrical self-shrinkers using Łojasiewicz inequalities.

In this article we prove that a connected and properly embedded translating soliton in $\mathbb{R}^3$ with uniformly bounded genus on compact sets which is $C^1$-asymptotic to two planes outside a cylinder, either is flat or coincides with the grim reaper cylinder.

Proves a Minkowski inequality for star-shaped hypersurfaces in warped cylinders.

For an orientable surface of finite type equipped with a flat metric with holonomy of finite order q, the set of maximal embedded cylinders can be empty, non-empty, finite, or infinite. The case when q < 3 is well-studied as such surfaces are (semi-)translation surfaces. Not only is the set always infinite, the core cu…

We cut a hyperbolic surface of finite area along some analytic simple closed curves, and glue in cylinders of varying moduli. We prove that as the moduli of the glued cylinders go to infinity, the Fenchel-Nielsen twist coordinates for the resulting surface around those cylinders converge.

New method proves inequalities for self-shrinkers using perturbation.

We give a Dehn-Nielsen type theorem for the homology cobordism group of homology cylinders by considering its action on the acyclic closure, which was defined by Levine, of a free group. Then we construct an additive invariant of those homology cylinders which act on the acyclic closure trivially. We also describe some…

We derive all possible causality conditions for conformally flat Lorentzian metrics on the two-dimensional cylinder.

A homology cylinder over a surface consists of a homology cobordism between two copies of the surface and markings of its boundary. The set of isomorphism classes of homology cylinders over a fixed surface has a natural monoid structure and it is known that this monoid can be seen as an enlargement of the mapping class…

Research shows curves in Walker 3-manifolds can lie in flat cylinders.

In the previous paper, the structure of the cut locus was determined for a class of surfaces of revolution homeomorphic to a cylinder. In this paper, we prove the structure theorem of the cut locus for a wider class of surfaces of revolution homeomorphic to a cylinder.

Smooth convergence to an enveloping cylinder proved for mean curvature flow of complete graphical hypersurfaces.

The homology cobordism group of homology cylinders is a generalization of the mapping class group and the string link concordance group. We study this group and its filtrations by subgroups by developing new homomorphisms. First, we define extended Milnor invariants by combining the ideas of Milnor's link invariants an…

We show that some pieces of cylinders bounded by two parallel straight-lines bifurcate in a family of periodic non-rotational surfaces with constant mean curvature and with the same boundary conditions. These cylinders are initial interfaces in a problem of microscale range modeling the morphologies that adopt a liquid…

We prove a sharp lower bound on the curvatures of non-flat ASD connections over the cylinder.

Let S be a compact connected oriented surface, whose boundary is connected or empty. A homology cylinder over the surface S is a cobordism between S and itself, homologically equivalent to the cylinder over S. The Y-filtration on the monoid of homology cylinders over S is defined by clasper surgery. Using a functorial …

New discrete models for constant mean curvature surfaces and tori.