arXiv research

Method for generating new curves from plane curves on cylinders.

In this paper we investigate constant mean curvature surfaces with nonempty boundary in Euclidean space that meet a right cylinder at a constant angle along the boundary. If the surface lies inside of the cylinder, we obtain some results of symmetry by using the Alexandrov reflection method. When the mean curvature is …

We prove that globally subanalytic nonsingular CMC surfaces of $\mathbb{R}^3$ are only planes, round spheres or right circular cylinders

The paper studies a 1D diffusion equation with nonlinear Robin boundary conditions and finds conditions for global and finite time blow-up or blow-down.

In this paper we consider the isoperimetric profile of convex cylinders $K\times\mathbb{R}^q$, where $K$ is an $m$-dimensional convex body, and of cylindrically bounded convex sets, i.e, those with a relatively compact orthogonal projection over some hyperplane of $\mathbb{R}^{n+1}$, asymptotic to a right convex cylind…

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…

This paper establishes an interesting connection between the family of CMC surfaces of revolution in $\mathbb E_1^3$ and some specific families of elliptic curves. As a consequence of this connection, we show in the class of spacelike CMC surfaces of revolution in the $\mathbb E_1^3$, only spacelike cylinders and stand…

Let $D$ be any elliptic right cylinder. We prove that every type of knot can be realized as the trajectory of a ball in $D.$ This proves a conjecture of Lamm and gives a new proof of a conjecture of Jones and Przytycki. We use Jacobi's proof of Poncelet's theorem by means of elliptic functions.

Solves the gauge problem for Ricci flow cylinders, proving strong rigidity.

Study on helicoidal singular minimal surfaces with specific properties.

The paper proposes a conjecture for a symmetric version of Ehrhard's inequality.

We study the Gauss map $G$ of surfaces of revolution in the 3-dimensional Euclidean space ${\mathbb{E}^3}$ with respect to the so called Cheng-Yau operator $\square$ acting on the functions defined on the surfaces. As a result, we establish the classification theorem that the only surfaces of revolution with Gauss map …

Minimal cylinders in Heisenberg group characterized using loop group method.

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.

Simplified computation of SFT invariants for Legendrian links.

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 …

Study proves rigidity of specific self-shrinkers under certain geometric conditions.

Let $f:M\to \mathbb{R}$ be a Morse function on a connected compact surface $M$, and $\mathcal{S}(f)$ and $\mathcal{O}(f)$ be respectively the stabilizer and the orbit of $f$ with respect to the right action of the group of diffeomorphisms $\mathcal{D}(M)$. In a series of papers the first author described the homotopy t…

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…

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…

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…

Study on spin-zero rest-mass fields using conformal geometric method.

A homology cylinder over a compact manifold is a homology cobordism between two copies of the manifold together with a boundary parametrization. We study abelian quotients of the homology cobordism group of homology cylinders. For homology cylinders over general surfaces, it was shown by Cha, Friedl and Kim that their …

Holomorphic cylinders converge to disks joined by flow lines.

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…

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

Paper extends tree bijection for hyperbolic surfaces without requiring cusps.

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

The study examines invariants of homology cylinders and their relations to free nilpotent groups.

In the present paper we give a geometric proof for the existence of cylinders with constant mean curvature $H>H(X)$ in certain simply connected homogeneous three-manifolds $X$ diffeomorphic to $\mathbb{R}^3$, which always admit a Lie group structure. Here, $H(X)$ denotes the critical value for which constant mean curva…

The paper extends a knot invariant to graphs and connects it to homology cylinders.

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…

New steady Kähler-Ricci solitons found on orbifolds.

Cylinders in warped product spaces have zero curvature.

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

The study characterizes hypersurfaces in weighted cylinders and generalizes confinement properties.

We show that timelike maximal cylinders in $\RR^{1 + 2}$ always develop singularities in finite time and that, infinitesimally at a generic singularity, their time slices are evolved by a rigid motion or a self-similar motion. We also prove a mild generalization in non-flat backgrounds.

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.

In this paper, we prove gap results for constant mean curvature (CMC) surfaces. Firstly, we find a natural inequality for CMC surfaces which imply convexity for distance function. We then show that if $Σ$ is a complete, properly embedded CMC surface in the Euclidean space satisfying this inequality, then $Σ$ is either …

Study decomposes geometric surfaces, finding special curves.

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

Classifies quantum particle behavior on a special cylinder.

Construct minimal Lagrangian surfaces in complex projective plane via loop group method.

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

The paper classifies translation surfaces with constant curvature in a specific connection.

Study finds solutions to inequality decay to zero on warped cylinders.

Stable cylinders found in hyperbolic groups and curve graphs.