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.
Weyl's tube formula holds for various cross-sections under symmetry conditions.
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.
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.
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.
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 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.
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.
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.
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.
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…
The paper characterizes D'Atri spaces using total scalar curvature of hemispheres.
The study examines constant mean curvature tubes around geodesics in specific 3-manifolds.
New theory classifies knotted spheres in 4D space.
We study the complete Kahler-Einstein metric in tube domains. We obtain estimates of this metric and its holomorphic bisectional curvatures near the weakly pseudoconvex boundary points.
A formula of the renormalized volume of tubes over polalized Kähler-Einstein manifolds is given in terms of the Einstein constant and the volume of the polarization.
Researchers prove a complex geometric conjecture about certain manifolds.
Tubes in manifolds require wide spaces.
As this is for the Bulletin of the A.M.S., it is not only a review of Alexander Isaev's Spherical Tube Hypersurfaces but also a brief introduction to CR geometry.
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…
Study on conditions for singular local tube fibrations.
This short paper is based on the talk of the second author given at the 2005 Hayama Symposium on Complex Analysis in Several Variables. The recent results of the authors on the spectrum of quantum tubes are summarized.
Proves Steiner and tube formulae for 3D contact sub-Riemannian surfaces.
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.
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 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.
The study proves a tube theorem for complex hyperbolic manifolds.