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.
Fundamental solutions found for p-Laplace equations in Heisenberg and Grushin spaces.
New cylindrical solutions found for Grushin-type problem.
We employ Grushin jets which are adapted to the geometry of Grushin-type spaces to obtain the existence-uniqueness of viscosity solutions to the -Laplace equation in Grushin-type spaces. Due to the differences between Euclidean jets and Grushin jets, the Euclidean method of proof is not valid in this environ…
We study the problem of so-called geometric quantum confinement in a class of two-dimensional incomplete Riemannian manifold with metric of Grushin type. We employ a constant-fibre direct integral scheme, in combination with Weyl's analysis in each fibre, thus fully characterising the regimes of presence and absence of…
Study on heat flow across two half-lines with special boundary conditions.
Extensions of Brownian motion to singular surfaces are studied.
We prove a classification theorem for conformal maps with respect to the control distance generated by a system of diagonal vector fields. It turns out that all such maps can be obtained as compositions of suitable dilations, inversions and isometries. We also classify all umbilical surfaces of the underlying metric.
Paper studies viscosity solutions in unique Martinet spaces.
We find the fundamental solution to the p-Laplace equation in a class of Hörmander vector fields that generate neither a Carnot group nor a Grushin-type space. The singularity occurs at the sub-Riemannian points which naturally corresponds to finding the fundamental solution of a generalized operator in Euclidean space…
Classifies quantum particle behavior on a special cylinder.
The study examines optimal synthesis in a radially symmetric Grushin space with conditions on the weight function.
We establish a Harnack inequality for a class of quasi-linear PDE modeled on the prototype {equation*} \partial_tu= -\sum_{i=1}^{m}X_i^\ast (|\X u|^{p-2} X_i u){equation*} where , $ \ \X = (X_1,..., X_m)$ is a system of Lipschitz vector fields defined on a smooth manifold $\M$ endowed with a Borel measure , …
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 extends curve curvature types from normed to gauge planes.
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.
Study compact plane waves, showing they are essentially standard.
New harmonic maps to hyperbolic plane via Bäcklund transformation.
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 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…
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.
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. …
New combinatorial type helps distinguish plane curve topologies.
Curve shortening in metric-affine plane shrinks convex curves to points.
The paper characterizes Ricci solitons on the Poincaré upper half plane.
Method for generating new curves from plane curves on cylinders.