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 calculates rational homology groups of configuration spaces for a Moebius strip and a projective plane.
We construct real analytic flat Moebius strips of arbitrary isotopy types, whose centerlines are geodesics or lines of curvature.
Motivated by the problem of finding an explicit description of a developable narrow Moebius strip of minimal bending energy, which was first formulated by M. Sadowsky in 1930, we will develop the theory of elastic strips. Recently E.L. Starostin and G.H.M. van der Heijden found a numerical description for an elastic Mo…
The study constructs equivariant harmonic maps into symmetric spaces with applications to Willmore surfaces.
The geometry and topology of complete nonorientable maximal surfaces with lightlike singularities in the Lorentz-Minkowski 3-space are studied. Some topological congruence formulae for surfaces of this kind are obtained. As a consequence, some existence and uniqueness results for maximal Moebius strips and maximal Klei…
The paper constructs graph models for n-dimensional manifolds.
A hypersurface without umbilics in the n+1 dimensional Euclidean space is known to be determined by the Moebius metric and the Moebius second fundamental form up to a Moebius transformation when n>2. In this paper we consider Moebius rigidity for hypersurfaces and deformations of a hypersurface preserving the Moebius m…
In this paper we study Moebius applicable surfaces, i.e., conformally immersed surfaces in Moebius 3-space which admit deformations preserving the Moebius metric. We show new characterizations of Willmore surfaces, Bonnet surfaces and Harmonic inverse mean curvature surfaces in terms of Moebius or similarity invariants…
This paper classifies flat submanifolds with a special type of curvature form.
Completes the classification of Moebius deformable hypersurfaces for dimensions 5 and above.
A Moebius structure (on a set X) is a class of metrics having the same cross-ratios. A Moebius structure is ptolemaic if it is invariant under inversion operations. The boundary at infinity of a CAT(-1) space is in a natural way a Moebius space, which is ptolemaic. We give a free of classification proof of the followin…
Together with the Moebius strip, the Klein bottle is one of the intriguing objects in the universe of geometry, sometimes appearing in non-mathematical contexts too. Until now, several parametrizations of it as a surface immersed in ordinary three-space have been found, some of which are very elegant and lead to nice a…
New theorem on embedding Moebius bands in 3D space.
Improved bound for optimal Moebius band aspect ratio.
Classifies special submanifolds with specific curvature properties.
New method classifies hypersurfaces that can bend infinitesimally.
The paper initiates a systematic study of Moebius structures and Ptolemy spaces. We conjecture that every compact Ptolemy space with circles and many space inversions is Moebius equivalent to the boundary at infinity of a rank one symmetric space of noncompact type. We prove this conjecture for the class of complex hyp…
Extension of Moebius maps to CAT(-1) spaces using circumcenters.
We prove that every knot in the 3-space bounds an embedded punctured Moebius band whose other boundary component is a quasipositive fibred knot.
Moebius rigidity proven for negatively curved surfaces without cocompactness.
Paper classifies special Euclidean hypersurfaces with specific geometric properties.
O. Kobayashi in 2007 proved that differentiable mappings preserving anharmonic ratio are Moebius transformations. We strengthen his result and prove, that the requirement of differentiability and even of injectivity can be omitted.
Lectures on Moebius-Lie geometry and its extension, including new geometric ensembles.
Knotted trivalent graphs (KTGs) form a rich algebra with a few simple operations: connected sum, unzip, and bubbling. With these operations, KTGs are generated by the unknotted tetrahedron and Moebius strips. Many previously known representations of knots, including knot diagrams and non-associative tangles, can be tur…
Wintgen ideal submanifolds in space forms are those ones attaining equality at every point in the so-called DDVV inequality which relates the scalar curvature, the mean curvature and the normal scalar curvature. This property is conformal invariant; hence we study them in the framework of Moebius geometry, and restrict…
Moebius-Kantor graph connects multiple groups and topological properties.
Proves an Euler-type formula for Möbius strip partitions.
Motivated by the theory of quantum waveguides, we investigate the spectrum of the Laplacian, subject to Dirichlet boundary conditions, in a curved strip of constant width that is defined as a tubular neighbourhood of an infinite curve in a two-dimensional Riemannian manifold. Under the assumption that the strip is asym…
We introduce the notion of strip complex. A strip complex is a special type of complex obtained by gluing "strips" along their natural boundaries according to a given graph structure. The most familiar example is the one dimensional complex classically associated with a graph, in which case the strips are simply copies…
A submanifold in a real space form attaining equality in the DDVV inequality at every point is called a Wintgen ideal submanifold. They are invariant objects under the Moebius transformations. In this paper, we classify those Wintgen ideal submanifolds of dimension m>3 which are Moebius homogeneous. There are three cla…
Compact negatively curved manifolds with Moebius rigidity.
Effective quantum dynamics on a thin Möbius strip approximated by a flat model.
Study on quantum strips in higher dimensions, focusing on essential and discrete spectra.
A simpler 3D Möbius strip design without twists.
Plateau's problem is to show the existence of an area minimizing surface with a given boundary, a problem posed by Lagrange in 1760. Experiments conducted by Plateau showed that an area minimizing surface can be obtained in the form of a film of oil stretched on a wire frame, and the problem came to be called Plateau's…
Continuous family of maps extends Moebius homeomorphisms between hyperbolic spaces.
In a previous preprint we defined an energy associated to every embedding of a surface into or . This energy is invariant under Moebius tranformations and the "round" sphere is its only absolute minimum. Here we sketch a proof of the compactness property for a variant of it. The details will appear elsewhere…
For a m-tuple a=(a_1,...,a_m) of positive real numbers, the robot arm of type a in R^d is the map f^a:(S^{d-1})^m -> R^d defined by f^a(z_1,...,z_m) to be the sum of the a_jz_j's. Our aim is to attack the inverse problem via the horizontal liftings for the distribution Delta^a orthogonal to the fibers of f^a. One shows…
The Moebius energy of a knot is an energy functional for smooth curves based on an idea of self-repelling. If a knot has a thick tubular neighborhood, we would intuitively expect the energy to be low. In this paper, we give explicit bounds for energy in terms of the ropelength of the knot, i.e. the ratio of the length …
Study strip deformations of hyperbolic polygons with decorated vertices.
Solves Dirichlet problem for translating solitons in a strip.
Given a topological space X denote by exp_k(X) the space of non-empty subsets of X of size at most k, topologised as a quotient of X^k. This space may be regarded as a union over 0 < l < k+1 of configuration spaces of l distinct unordered points in X. In the special case X=S^1 we show that: (1) exp_k(S^1) has the homot…
Ancient solutions on a strip are constant if polynomial, and have finite-dimensional space for slower growth.
We prove a flat strip theorem for 2-dimensional ptolemaic spaces.
Formula removes geometric patterns from random hyperbolic surfaces.
New method weaves paper strips for designing curved surfaces with elasticity.
I give a theory of Moebius-flat hypersurfaces in n-dimensional projective space, analogous to that in conformal geometry. This unifies the classes of hypersurfaces with flat induced conformal structure (n > 3) and a classically studied class of surfaces (n = 3). I extend an example of Akivis-Konnov, and use polynomial …
The strip map is a natural map from the arc complex of a bordered hyperbolic surface to the vector space of infinitesimal deformations of . We prove that the image of the strip map is a convex hypersurface when is a surface of small complexity: the punctured torus or thrice punctured sphere.