arXiv research

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

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

The aim of this note is to explain a generalization to the real case of a well known result on the automorphism group of an unbounded tube type symmetric domain in a complex vector space of finite dimension.

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 …

We consider the Johnson-Koranyi-Hua system on symmetric Siegel domains of type two. We prove that all functions which are annihilated by the system and satisfy an H^2 integrability condition are pluriharmonic. So the situation is completely different on type two domains than on tube type domains: it was proved by Johns…

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

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 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…

Sheng and Zuo's characteristic forms are invariants of a variation of Hodge structure. We show that they characterize Gross's canonical variations of Hodge structure of Calabi-Yau type over (Hermitian symmetric) tube domains.

We report on new numerical computations of the set of self-contacts in tightly knotted tubes of uniform circular cross-section. Such contact sets have been obtained before for the trefoil and figure eight knots by simulated annealing -- we use constrained gradient-descent to provide new self-contact sets for those and …

This paper studies finite type invariants for welded string links and ribbon tubes, showing characterizations and algebraic structures.

In this paper, we consider tubes in the Euclidean 3-space whose Gauss map n is of coordinate finite I-type, i.e., the position vector n satisfies the relation ΔIn = Λn, where ΔI is the Laplace operator with respect to the first fundamental form I of the surface and Λ is a square matrix of order 3. We show that circular…

Proves gap rigidity theorem for Hermitian symmetric spaces.

We classify tube domains in $\mathbb C^{n+1}$ ($n\ge 1$) with affinely homogeneous base of their boundary and a.) with positive definite Levi form and b.) with Lorentzian type Levi form and affine isotropy of dimension at least $\frac{(n-2)(n-3)}2$.

A knot K in 1-bridge position with respect to a genus-g Heegaard surface in a 3-manifold can be moved by isotopy through knots in 1-bridge position until it lies in a union of n parallel genus-g surfaces tubed together by n-1 straight tubes, with K intersecting each tube in two arcs connecting the ends. We prove that t…

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

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

The study examines constant mean curvature tubes around geodesics in specific 3-manifolds.

The study classifies hypersurfaces in quaternionic space forms with constant principal curvatures.

Proof of Knot Entropy Conjecture for tube lattice polygons.

Let $Γ$ be a nondegenerate geodesic in a compact Riemannian manifold $M$. We prove the existence of a partial foliation of a neighbourhood of $Γ$ by CMC surfaces which are small perturbations of the geodesic tubes about $Γ$. There are gaps in this foliation, which correspond to a bifurcation phenomenon. Conversely, we …

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

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.

Computes tube formulas for valuations in complex space forms.

In this article, we continue the classification of finite type Gauss map surfaces in the Euclidean 3-space E3 with respect to the first fundamental form by studying a subclass of tubes, namely the anchor rings. We show that anchor rings are of infinite type Gauss map.

The paper defines marginal tubes and proves their null nature.

Zero entropy found in entire Grauert tubes of certain manifolds.

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

Lower bound on boundary injectivity radius for specific tubes.

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 …

Study on entanglement complexity of confined ring polymers in lattice tubes.

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…

Study on volume of tubes and concentration in Riemannian geometry.

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 …

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.

Combines cost-sensitive and Neyman-Pearson paradigms for better binary classification.

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 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…

We show that a surface group contained in a reductive real algebraic group can be deformed to become Zariski dense, unless its Zariski closure acts transitively on a Hermitian symmetric space of tube type. This is a kind of converse to a rigidity result of Burger, Iozzi and Wienhard.

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.

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

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.