arXiv research

Study asymptotics of special curves on shrinking cylinders.

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

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

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

Study of Ricci flow on cylinders, proving longtime existence and asymptotic behavior.

Unique bowl soliton found as asymptotic to translating mean curvature flows.

Rotational symmetry proven for special self-expanders near cylinders.

The grim reaper cylinder is characterized for translating solitons in 3D.

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

Computes the contribution of one-cylinder square-tiled surfaces to Masur-Veech volumes.

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

Analyzes Hodge-Laplacian spectrum and de Rham cohomology on a cylinder-like manifold.

The paper proves rigidity of a specific 4D Ricci flow solution.

Characterizes translating solitons in R^(n+1) asymptotic to hyperplanes.

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

Flow of curved surfaces converges to a specific shape over time.

In this paper we prove that any asymptotically cylindrical gradient shrinking Ricci soliton is isometric to a cylinder.

This paper studies mean curvature flows near cylindrical singularities.

The paper constructs ancient solutions to curvature flows in bounded and unbounded regions.

Formulae count square-tiled surfaces in genus two.

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

The paper studies mean curvature flow with contact angles in high-dimensional cylinders.

Self-shrinkers in 3D have simple ends.

Unique hyperplanes are the only translating solitons asymptotic to half-hyperplanes.

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…

Study on instantons on cylinder manifolds with specific conditions.

Boundary bubbles form in almost minimal cylinders under specific conditions.

Sharp inscribed radius estimate for curved surfaces.

The paper studies the structure at infinity of shrinking Ricci solitons with bounded curvature.

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

The best known finite-time local Ricci flow singularity is the neckpinch, in which a proper subset of the manifold becomes geometrically close to a portion of a shrinking cylinder. In this paper, we prove precise asymptotics for rotationally symmetric Ricci flow neckpinches. We then compare these rigorous results with …

We explore the relationship between contact forms on $\mathbb S^3$ defined by Finsler metrics on $\mathbb S^2$ and the theory developed by H. Hofer, K. Wysocki and E. Zehnder in \cite{HWZ,HWZ1}. We show that a Finsler metric on $\mathbb S^2$ with curvature $K\geq 1$ and with all geodesic loops of length $>π$ is dynamic…

The study examines 4D steady gradient Ricci solitons with nonnegative curvature away from a compact set.

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 minimal surface problem in H^2xR.

Study spin-0 fields on n-dimensional Minkowski spacetimes, computing asymptotic charges.

Square-tiled surfaces with fixed combinatorics become equidistributed in moduli spaces.

We study the asymptotic behaviour of regularized determinants of certain Laplace type operators with respect to singular deformations of the underlying manifold which are obtained by stretching a tubular neighborhood of an embedded separating hypersurface to a cylinder of infinite length. Using the asymptotic expansion…

New model for STSs with restricted horizontal gluings, focusing on maximal horizontal cylinders.

The study proves uniqueness of certain types of solitons.

For any asymptotically conical self-shrinker with entropy less than or equal to that of a cylinder we show that the link of the asymptotic cone must separate the unit sphere into exactly two connected components, both diffeomorphic to the self-shrinker. Combining this with recent work of Brendle, we conclude that the r…

This paper studies symplectic vortices on compact manifolds, proving their asymptotic behavior.

We prove that for a 7-dimensional manifold M with cylindrical ends the moduli space of exponentially asymptotically cylindrical torsion-free G_2 structures is a smooth manifold (if non-empty), and study some of its local properties. We also show that the holonomy of the induced metric of an exponentially asymptotically…

Asymptotically cylindrical Ricci-flat manifolds play a key role in constructing Topological Quantum Field Theories. It is particularly important to understand their behavior at the cylindrical ends and the natural restrictions on the geometry. In this paper we show that an orientable, connected, asymptotically cylindri…

In the Cauchy problem for asymptotically flat vacuum data the solution-jets along the cylinder at space-like infinity develop in general logarithmic singularities at the critical sets at which the cylinder touches future/past null infinity. The tendency of these singularities to spread along the null generators of null…

Study finds many nonplanar minimal spheres in elongated ellipsoids.

Study on minimizing perimeter in unbounded convex bodies without boundary regularity.

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 …