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.
Using symplectic topology and the Radon transform, we prove that smooth 4-dimensional projective planes are diffeomorphic to . We define the notion of a plane curve in a smooth projective plane, show that plane curves in high dimensional regular planes are lines, prove that homeomorphisms preserving plan…
We define generalized distance-squared mappings, and we concentrate on the plane to plane case. We classify generalized distance-squared mappings of the plane into the plane in a recognizable way.
The study classifies semiaffine stable planes into affine, projective, or punctured projective planes.
Stable planes are locally isomorphic to classical projective planes.
Only vertical planes are asymptotic to other planes in 3D space.
Study of elementary planes in Apollonian orbifold with unusual equidistribution.
Generic smooth plane-to-plane map germs are topologically equivalent to cones of mappings of the circle. We carry out a complete topological classification of smooth stable mappings of the circle and show how this classification leads, via the result mentioned above, to a topological classification of finitely determin…
Criteria for sharksfin and deltoid singularities from plane to plane, with applications.
We study two types of isotropic planes: weakly isotropic and strongly isotropic planes. We prove that a Riemannian manifold of indefinite metric is conformally flat if and only if its curvature tensor vanishes on all the strongly isotropic planes. We specialize the plane axiom for Riemannian manifolds of indefinite met…
The study explores conformal planes with finite areas.
For a pair of points in a smooth locally convex surface in 3-space, its mid-plane is the plane containing its mid-point and the intersection line of the corresponding pair of tangent planes. In this paper we show that the limit of mid-planes when one point tends to the other along a direction is the Transon plane of th…
We construct a compact nonpositively curved squared 2-complex whose universal cover contains a flat plane that is not the limit of periodic flat planes.
This thesis explores bifoliated planes and their group actions from Anosov flows.
We use reduced homogeneous coordinates to study Riemannian geometry of the octonionic (or Cayley) projective plane. Our method extends to the para-octonionic (or split octonionic) projective plane, the octonionic projective plane of indefinite signature, and the hyperbolic dual of the octonionic projective plane; we di…
Two proofs show that removing a loop from a plane circuit splits the plane.
The paper classifies singularities of plane congruences and affine distance functions.
Computed distortion coefficients for the α-Grushin plane.
New findings on plane waves in 3D spacetimes, showing non-unimodular elliptic plane waves are unique.
New harmonic maps to hyperbolic plane via Bäcklund transformation.
Study compact plane waves, showing they are essentially standard.
The paper examines asymptotic lines of plane fields in 3D space.
A 6-regular triangulation for hyperbolic plane created.
Study local and global aspects of complex plane curve embeddings.
A classical result asserts that the complex projective plane modulo complex conjugation is the 4-dimensional sphere. We generalize this result in two directions by considering the projective planes over the normed real division algebras and by considering the complexifications of these four projective planes.
A diffeomorphism of pseudo-Riemannian manifolds is called sectional curvature preserving if it preserves the sectional curvature of all the nondegenerate 2-planes. We consider a similar condition for degenerate 2-planes and we prove that the diffeomorphism is conformal (when the condition is fulfilled for weakly degene…
We study a moduli stratum of A-orbits of plane-to-plane germs of corank 2 with codimension 3. We describe explicitly the bifurcation diagram of its topologically A-versal unfolding. Two geometric applications to parabolic objects are presented.
We shall give useful criteria of lips, beaks and swallowtail singularities of smooth map from the plane into the plane. As an application of criteria, we will discuss the singularities of Cauchy problem of single conservation law.
Proves conjecture about geodesic foliations in Riemannian planes.
Stochastic cutting planes improve data-driven optimization speed.
The paper characterizes coverings over the projective plane with minimal defect.
We study rays in von Mangoldt planes, which has applications to the structure of open complete manifolds with lower radial curvature bounds. We prove that the set of souls of any rotationally symmetric plane of nonnegative curvature is a closed ball, and if the plane is von Mangoldt, we compute the radius of the ball. …
Curve shortening in metric-affine plane shrinks convex curves to points.
New combinatorial type helps distinguish plane curve topologies.
The paper characterizes Ricci solitons on the Poincaré upper half plane.
Method for generating new curves from plane curves on cylinders.
The study examines vertices in curves with singular points in the Euclidean plane.
New flat Minkowski planes created from convex functions.
Solves four problems related to circle families in the plane.
Schenkel proved that the automorphism group of a flat Minkowski plane is a Lie group of dimension at most 6 and described planes whose automorphism group has dimension at least 4 or one of whose kernels has dimension 3. We extend these results to the case of toroidal circle planes.
In this paper results from the differential geometry of curves are extended from normed planes to gauge planes which are obtained by neglecting the symmetry axiom. Based on the gauge analogue of the notion of Birkhoff orthogonality from Banach space theory, we study all curvature types of curves in gauge planes, thus g…
A mathematical paradox shows secant planes don't always form a tangent plane, but some analogies hold with a specific vector product.
A relation between the Goldstein-Petrich hierarchy for plane curves and the Toda lattice hierarchy is investigated. A representation formula for plane curves is given in terms of a special class of -functions of the Toda lattice hierarchy. A representation formula for discretized plane curves is also discussed.
Study on isoperimetric problem in Randers planes achieving maximum area.
For any chord diagram on a circle there exists a complete graph on sufficiently many vertices such that any generic immersion of it to the plane contains a plane closed curve whose chord diagram contains the given chord diagram as a sub-chord diagram. For any generic immersion of the complete graph on six vertices to t…
Characterizes pseudo-Anosov orbit spaces via bifoliated planes
The paper uses complex-valued functions to simplify plane differential geometry and kinematics.
The study finds bounds on metrics with constant curvature in the plane.
The paper describes handle decompositions and Kirby diagrams for plane algebraic curves.