arXiv research

Extends decay estimates for Yang-Mills-Higgs fields on Minkowski and de Sitter spacetimes.

The study classifies quasi-Einstein manifolds with boundary.

Paper proves rigidity of certain Ricci shrinkers.

The paper studies Einstein submanifolds in Euclidean space and finds conditions for their properties.

This work concerns stability and instability of Einstein warped products with an Einsteinian fiber of codimension 1. We study the cases where the scalar curvature of the warped product and of the fiber are either both positive or both negative to complement the results in [Krö16]. Up to a small gap in the case of sin-c…

Twistor correspondences for R-invariant indefinite self-dual conformal structures on R^4 are established explicitly. These correspondences are written down by using a natural integral transform from functions on a two dimensional cylinder to functions on the flat Lorentz space R^{1,2} which is related to the wave equat…

The paper studies Kähler-Einstein metrics with singularities and their limits.

In this paper, we classify n-dimensional (n>3) complete Bach-flat gradient shrinking Ricci solitons. More precisely, we prove that any 4-dimensional Bach-flat gradient shrinking Ricci soliton is either Einstein, or locally conformally flat hence a finite quotient of the Gaussian shrinking soliton $R^4$ or the round cyl…

A well-known result asserts that any isometric immersion with flat normal bundle of a Riemannian manifold with constant sectional curvature into a space form is (at least locally) holonomic. In this note, we show that this conclusion remains valid for the larger class of Einstein manifolds. As an application, when assu…

The study examines biharmonic hypersurfaces in a product space and finds conditions for their minimal or cylinder forms.

In this paper we study the behavior of the Ricci flow at infinity for the full flag manifold $SU(3)/T$ using techniques of the qualitative theory of differential equations, in special the Poincaré Compactification and Lyapunov exponents. We prove that there are four invariant lines for the Ricci flow equation, each one…

Paper proves rigidity of Poincaré-Einstein manifolds with cylindrical conformal infinities.

Study on renormalized volume of minimal submanifolds in Poincare-Einstein manifolds.

We present a general procedure to construct 6-dimensional manifolds with SU(3)-structure from SU(2)-structure 5-manifolds. We thereby obtain half-flat cylinders and sine-cones over 5-manifolds with Sasaki-Einstein SU(2)-structure. They are nearly Kahler in the special case of sine-cones over Sasaki-Einstein 5-manifolds…

We prove that a gradient shrinking Ricci soliton with fourth order divergence-free Riemannian tensor is rigid. For the $4$-dimensional case, we show that any gradient shrinking Ricci soliton with fourth order divergence-free Riemannian tensor is either Einstein, or a finite quotient of the Gaussian shrinking soliton $\…

The paper proves strong uniqueness and rectifiability of generalized cylindrical singularities in Ricci flow.

The paper classifies λ-biharmonic hypersurfaces in product spaces.

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 …

In this paper we provide a new method for establishing the rotational symmetry of the solutions to a couple of very classical overdetermined problems arising in potential theory, in both the exterior and the interior punctured domain. Thanks to a conformal reformulation of the problems, we obtain Riemannian manifolds w…

New cohomology vanishing result for twisted cylinders.

Constructs initial data for Einstein equations and estimates Bartnik mass outside time-symmetry.

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.

The paper studies cylinder curves in flat metrics with q > 2.

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

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

We study biharmonic hypersurfaces in a generic Riemannian manifold. We first derive an invariant equation for such hypersurfaces generalizing the biharmonic hypersurface equation in space forms studied in \cite{Ji2}, \cite{CH}, \cite{CMO1}, \cite{CMO2}. We then apply the equation to show that the generalized Chen's con…

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

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.

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

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…

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…