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.
The paper defines marginal tubes and proves their null nature.
We show that the maximal future development of asymptotically flat spherically symmetric black hole initial data for a self-gravitating nonlinear scalar field, also called a Higgs field, contains a connected, achronal marginally trapped tube which is asymptotic to the event horizon of the black hole, provided the initi…
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 …
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 be bounded…
We give conditions on a general stress-energy tensor T_{αβ} in a spherically symmetric black hole spacetime which are sufficient to guarantee that the black hole will contain a (spherically symmetric) marginally trapped tube which is eventually achronal, connected, and asymptotic to the event horizon. Price law decay p…
Study proves existence of MOTTs in de Sitter spacetime.
Small deformations of marginally (outer) trapped surfaces are considered by using their stability operator. In the case of spherical symmetry, one can use these deformations on any marginally trapped round sphere to prove several interesting results. The concept of 'core' of a black hole is introduced: it is a minimal …
Small deformations of marginally outer trapped surfaces (MOTS) are studied by using the stability operator introduced by Andersson-Mars-Simon. Novel formulae for the principal eigenvalue are presented. A characterization of the many marginally outer trapped tubes (MOTT) passing through a given MOTS is given, and the po…
Weyl's tube formula holds for various cross-sections under symmetry conditions.
We solve Einstein vacuum equations in a spacetime region up to the "center" of gravitational collapse. Within this region, we construct a sequence of marginally outer trapped surfaces (MOTS) with areas going to zero. These MOTS form a marginally outer trapped tube (apparent horizon). It emerges from a point and is smoo…
Computes tube formulas for valuations in complex space forms.
The purpose of the present work is to study (marginally) trapped submanifolds lying in a null hypersurface. Let $(M,g,N)\to\Bm(c)$ be a null hypersurface of a space-time with constant sectional curvature , endowed with a Screen Integrable and Conformal rigging . The (Marginally) Trapped Submanifolds we are intere…
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.