arXiv research

New method for flexible tubes and structures, enabling rigid-foldability.

Lower bound on boundary injectivity radius for specific tubes.

We prove that elliptic tubes over properly convex domains of the real projective space are C-convex and complete Kobayashi-hyperbolic. We also study a natural construction of complexification of convex real projective manifolds.

We construct an example of a spherically symmetric black hole interior in which there is NO (spherically symmetric) marginally trapped tube asymptotic to the event horizon. The construction uses a self-gravitating massive scalar field matter model, and the key condition we impose is that the scalar field $φ$ be bounded…

The study shows that the visible range from a point on harmonic manifolds follows an exponential distribution.

Weyl's tube formula holds for various cross-sections under symmetry conditions.

We study the canonical complexifications of non-compact Riemannian symmetric spaces G/K by the Grauert tube construction. We determine the maximal such complexification, a domain already constructed in another context by Akhiezer and Gindikin (Math. Ann., 1990), and show that this domain is Stein. We show there is an a…

Computes tube formulas for valuations in complex space forms.

The paper defines marginal tubes and proves their null nature.

Study proves certain Zoll manifolds with entire Grauert tubes are isometric.

Zero entropy found in entire Grauert tubes of certain manifolds.

Partial answer to affineness of entire Grauert tubes, with Stein manifold criterion.

H. Hotelling proved that in the n-dimensional Euclidean or spherical space, the volume of a tube of small radius about a curve depends only on the length of the curve and the radius. A. Gray and L. Vanhecke extended Hotelling's theorem to rank one symmetric spaces computing the volumes of the tubes explicitly in these …

Let $f:M^m\longrightarrow \Bbb R^{m+k}$ be an immersion where $M$ is a smooth connected $m$-dimensional manifold without boundary. Then we construct a subspace $Ω(f)$ of $\mathbb{R}^k$, namely push-out space. which corresponds to a set of embedded manifolds which are either parallel to $f$, tubes around $f$ or, in…

In the present paper we provide new examples of marginally trapped surfaces and tubes in FLRW spacetimes by using a basic relation between these objects and CMC surfaces in 3-manifolds. We also provide a new method to construct marginally trapped surfaces in closed FLRW spacetimes, which is based on the classical Hopf …

Zoll manifolds with entire Grauert tubes are proven to be standard complex projective spaces.

A compact real analytic Riemannian manifold M admits a canonical complexification with plurisubharmonic exhaustion function satisfying the homogeneous complex Monge-Ampere equation, called a Grauert tube. From the point of view of complex analysis, several authors have considered whether a given complex manifold can ar…

The Weyl tube theorem is extended to Kähler manifolds.

Study on volume of tubes and concentration in Riemannian geometry.

Study equivariant 4-genus of knots in symmetric 4-manifolds.

A surface is called a tube if its level-sets with respect to some coordinate function (the axis of the surface) are compact. Any tube of zero mean curvature has an invariant, the so-called flow vector. We study how the geometry of the Gaussian image of a higher-dimensional minimal tube M is controlled by the angle alph…

We deliver examples of non-Gromov hyperbolic tube domains with convex bases (equipped with the Kobayashi distance). This is shown by providing a criterion on non-Gromov hyperbolicity of (non-smooth) domains.The results show the similarity of geometry of the bases of non-Gromov hyperbolic tube domains with the geometry …

We define a Toledo number for actions of surface groups and complex hyperbolic lattices on infinite dimensional Hermitian symmetric spaces, which allows us to define maximal representations. When the target is not of tube type we show that there cannot be Zariski-dense maximal representations, and whenever the existenc…

In this paper, we investigate the volume-prserving mean curvature flow starting from a tube (of nonconstant radius) over a compact closed domain of a reflective submanifold in a symmetric space. We prove that the tubeness is preserved along the flow under certain conditions.

We consider an example of tubes of hypersurfaces in Euclidean space and generalise the tube formula to supercase. By this we assign to a point of the hypersurface in superspace a rational characteristic function. Does this rational function appear when we calculate the zeta-function of an arithmetic variety?

We classify the torsion pairs in a tube category and show that they are in bijection with maximal rigid objects in the extension of the tube category containing the Pruefer and adic modules. We show that the annulus geometric model for the tube category can be extended to the larger category and interpret torsion pairs…

We obtain upper bounds for the first Dirichlet eigenvalue of a tube around a complex submanifold $P$ of $CP^n$ which depends only on the radius of the tube, the degrees of the polynomials defining $P$ and the first eigenvalue of some model centers of the tube. The bounds are sharp on these models. Moreover, when the mo…

Let M be a real analytic Riemannian manifold. An adapted complex structure on TM is a complex structure on a neighborhood of the zero section such that the leaves of the Riemann foliation are complex submanifolds. This structure is called entire if it may be extended to the whole of TM. We call such manifolds Grauert t…

In this paper, we establish a rigorous correspondence between the two tube algebras, that one comes from the Turaev-Viro-Ocneanu TQFT introduced by Ocneanu and another comes from the sector theory introduced by Izumi, and construct a canonical isomorphism between the centers of the two tube algebras, which is a conjuga…

We construct and identify star representations canonically associated with holonomy reducible simple symplectic symmetric spaces. This leads the a non-commutative geometric realization of the correspondence between causal symmetric spaces of Cayley type and Hermitian symmetric spaces of tube type.

Estimates Betti numbers of loop spaces of compact manifolds.

In this paper, we study the spectrum of quantum tubes. Under certain intrinsic assumptions of the asymptotically flat submanifold of the Euclidean space, we prove the existence of the ground state of the quantum tube. The work is a generalization of Duclos, Exner and Krejcirik (CMP, 223(1), 13-28, 2001) and ourselves(m…

Researchers solved a geometry paradox for creased tubes.

Study infinite Euclidean distance discriminants of algebraic varieties.

We give a geometric model for a tube category in terms of homotopy classes of oriented arcs in an annulus with marked points on its boundary. In particular, we interpret the dimensions of extension groups of degree 1 between indecomposable objects in terms of negative geometric intersection numbers between correspondin…

New formula for curvatures of curves in n-dimensional space.

Extends Satoh's map to virtual m-links and constructs geometric pictures.

To every real analytic Riemannian manifold M there is associated a complex structure on a neighborhood of the zero section in the real tangent bundle of M. This structure can be uniquely specified in several ways, and is referred to as a Grauert tube. We say that a Grauert tube is entire if the complex structure can be…

Explicit Taylor series for the volume of tubes in Lie groups

We give sharp, effective bounds on the distance between tori of fixed injectivity radius inside a Margulis tube in a hyperbolic 3-manifold.

We establish the adiabatic dissapearance of Seiberg-Witten tunnelings on tubes R x N, where N is an S^1 fibration over a Riemann surface.

First we investigate the evolutions of the radius function and its gradient along the volume-preserving mean curvature flow starting from a tube (of nonconstant radius) over a compact closed domain of a reflective submanifold in a symmetric space under certain condition for the radius function. Next, we prove that the …

Study constant mean curvature tubes in homogeneous spaces.

The paper classifies hypersurfaces with special curvature properties in various spaces.

We obtain various estimates of the life-time of two-dimensional minimal tubes in R^3 by potential theory methods.

The Dirichlet Laplacian in curved tubes of arbitrary cross-section rotating with respect to the Tang frame along infinite curves in Euclidean spaces of arbitrary dimension is investigated. If the reference curve is not straight and its curvatures vanish at infinity, we prove that the essential spectrum as a set coincid…

Study proves existence of MOTTs in de Sitter spacetime.

We show that the boundaries of thin strongly pseudoconvex Grauert tubes, with respect to the Guillemin-Stenzel Kähler metric canonically associated with the Poincaré metric on closed hyperbolic real-analytic surfaces, has nowhere vanishing Cartan CR-curvature. This result provides a wealth of examples of compact $3$-di…