A locally-built, LLM-digested index of recent arXiv papers in quant finance, geometry/topology, and statistical ML — keyword search served straight from SQLite on this machine.
Study on conditions for singular local tube fibrations.
New theory classifies knotted spheres in 4D space.
This note investigates the so-called Tube map which connects welded knots, that is a quotient of the virtual knot theory, to ribbon torus-knots, that is a restricted notion of fillable knotted tori in the 4-sphere. It emphasizes the fact that ribbon torus-knots with a given filling are in one-to-one correspondence with…
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…
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…
Bounded symmetric domains are biholomorphic to tube domains over Finsler symmetric cones.
New method normalizes Milnor fibrations for real analytic maps.
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.
We give positive answers for questions by Berestovskii. Namely, we prove that every bijection of locally compact geodesically complete and connected at infinity CAT(0)-space onto itself preserving some fixed distance or satellite relations is an isometry of this space. The proof of this theorem is based on another …
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 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 …
Weyl's tube formula holds for various cross-sections under symmetry conditions.
Computes tube formulas for valuations in complex space forms.
The Weyl tube theorem is extended to Kähler manifolds.
Extends Satoh's map to virtual m-links and constructs geometric pictures.
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.
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 …
New method for flexible tubes and structures, enabling rigid-foldability.
Zoll manifolds with entire Grauert tubes are proven to be standard complex projective spaces.
Study on volume of tubes and concentration in Riemannian geometry.
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.
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…
During an operation of surgery on a Riemannian manifold and along a given embedded submanifold, one needs to replace the (old) metric induced by the exponential map on a tubular neighborhood of the submanifold by the Sasakian metric. So a good understanding of the behavior of these two metrics is important, this is our…
We obtain upper bounds for the first Dirichlet eigenvalue of a tube around a complex submanifold of which depends only on the radius of the tube, the degrees of the polynomials defining 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…
Estimates Betti numbers of loop spaces of compact manifolds.
Researchers solved a geometry paradox for creased tubes.
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…
When f : R power n to R power p, is a surjective real analytic map with isolated critical value, we prove that the (m)-regularity condition (in a sense we define) ensures that f ||f|| is a fibration on small spheres, f induces a fibration on the tubes and both fibrations are equivalent. In particular, we make the state…
We present the area and coarea formulas for Lipschitz maps, valid for general volume densities. As applications, we give a short, "euclidean" proof of the anisotropic Sobolev inequality and describe an anisotropic tube formula for hypersurfaces in . A discussion about the first variation of the anisotropic…
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.
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.
Study the topology of Milnor boundaries for real analytic map germs.
The paper explores meridional ranks of knotted surfaces and welded knots, proving equalities and relationships.
We obtain various estimates of the life-time of two-dimensional minimal tubes in R^3 by potential theory methods.
The study shows that the visible range from a point on harmonic manifolds follows an exponential distribution.