arXiv research

Boundary bubbles form in almost minimal cylinders under specific conditions.

Almost Zoll affine surface found on cylinder.

Study of origamis in minimal stratum with single cylinders, calculating spin parities and monodromy groups.

Minimal cylinders in Heisenberg group characterized using loop group method.

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

Paper proves almost rigidity theorem and applies it to study RCD(0,N) spaces.

Let G be a finitely presented group. Scott and Swarup have constructed a canonical splitting of G which encloses all almost invariant sets over virtually polycyclic subgroups of a given length. We give an alternative construction of this regular neighbourhood, by showing that it is the tree of cylinders of a JSJ splitt…

Consider a mean curvature flow of hypersurfaces in Euclidean space, that is initially graphical inside a cylinder. There exists a period of time during which the flow is graphical inside the cylinder of half the radius. Here we prove a lower bound on this period depending on the Lipschitz-constant of the initial graphi…

Constructs improperly embedded minimal disks with curvature issues.

The paper explores singular minimal translation graphs in Euclidean spaces.

The paper characterizes a helicoid in a cylinder with minimal area and unique boundary conditions.

The paper proves cylindrical nature of singular minimal ruled surfaces.

Minimal surfaces in S3(2) linked to vector fields on punctured sphere.

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

New theorem on 3-manifolds with curvature and convex boundary.

Study of degenerating maps to Riemannian manifolds, proving asymptotic limits and existence of minimal cylinders.

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 investigate minimal helix submanifolds of any dimension and codimension immersed in Euclidean space. Our main result proves that a ruled minimal helix submanifold is a cylinder. As an application we classify complex helix submanifolds of $\mathbb{C}^n$: They are extrinsic products with a complex line as a factor. Th…

New theorem splits 3-manifolds with non-negative curvature.

Study non-fillable curves in a hyperbolic surface with a real line.

New metrics found by attaching cylinders or cross caps to surfaces.

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

Study on helicoidal singular minimal surfaces with specific properties.

Study finds only first and second eigenvalues are Courant-sharp for flat Klein bottle and cylinders.

We define a geometric flow that is designed to change surfaces of cylindrical type spanning two disjoint boundary curves into solutions of the Douglas-Plateau problem of finding minimal surfaces with given boundary curves. We prove that also in this new setting and for arbitrary initial data, solutions of the Teichmüll…

Classifies quantum particle behavior on a special cylinder.

The paper proves geometric properties of square tables and saddle surfaces.

Solves minimal surface problem in H^2xR.

In this paper we study the mean curvature flow of embedded disks with free boundary on an embedded cylinder or generalised cone of revolution, called the support hypersurface. We determine regions of the interior of the support hypersurface such that initial data is driven to a curvature singularity in finite time or e…

Anosov subgroup equidistributes geodesics and holonomies on homogeneous spaces.

Random hyperbolic surfaces are mostly tangle-free, with geometric implications.

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

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

An Abelian differential gives rise to a flat structure (translation surface) on the underlying Riemann surface. In some directions the directional flow on the flat surface may contain a periodic region that is made up of maximal cylinders filled by parallel geodesics of the same length. The growth rate of the number of…

In this note a proof is given for global existence and uniqueness of minimal surfaces of Lorentzian type from a cylinder into globally hyperbolic Lorentzian manifolds for given initial values up to the first derivatives.

Gromov has shown how to construct holomorphic maps of the plane to a complex manifold with prescribed values on a lattice. In the present paper, a similar interpolation theorem for pseudo-holomorphic maps from the cylinder S to an almost-complex manifold (M,J) is proved. Properties of the space of pseudo-holomorphic ma…

In 1996, Nadirashvili used Runge's theorem to produce a complete minimal disc inside a ball in R^3. In this paper we generalize the techniques used by Nadirashvili to obtain new examples of complete minimal surfaces inside a ball in R^3, with the conformal structure of an annulus.

The paper explores conditions for certain submanifolds to be cylinders.

We give a sharp upper bound for the area of a minimal two-sphere in a three-manifold (M,g) with positive scalar curvature. If equality holds, we show that the universal cover of (M,g) is isometric to a cylinder.

Using a new method we give elementary estimates for the capacity of non-contractible annuli on cylinders and provide examples, where these inequalities are sharp. Here the lower bound depends only on the area of the annulus. In the case of constant curvature this lower bound is obtained with the help of a symmetrizatio…

In this note, we give natural extensions to cylinders and tori of a classical result due to T. Takahashi about minimal immersions into spheres. More precisely, we deal with Euclidean isometric immersions whose projections in R^N satisfy a spectral condition of their Laplacian.

Study on heat flow across two half-lines with special boundary conditions.

Minimal constructions of meanders and hyperelliptic pillowcase covers help in understanding ratio-optimizing pseudo-Anosovs.

Study finds many nonplanar minimal spheres in elongated ellipsoids.

The study proves that certain stable minimal hypersurfaces must be cylindrical.

Abelian differentials on Riemann surfaces can be seen as translation surfaces, which are flat surfaces with cone-type singularities. Closed geodesics for the associated flat metrics form cylinders whose number under a given maximal length generically has quadratic asymptotics in this length, with a common coefficient c…

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

Meyer and Reisner had proved the Mahler conjecture for rovelution bodies. In this paper, using a new method, we prove that among origin-symmetric bodies of revolution in R^3, cylinders have the minimal Mahler volume. Further, we prove that among parallel sections homothety bodies in R^3, 3-cubes have the minimal Mahler…