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 on Laplacian determinant in isosceles triangles, finding equilateral triangle minimizes determinant.
An edge tessellation is a tiling of the plane generated by reflecting a polygon in its edges. We prove that a polygon generating an edge tessellation is one the following eight types: a rectangle; an equilateral, 60-right, isosceles right, or 120-isosceles triangle; a 120-rhombus; a 60-90-120 kite; or a regular hexagon…
Study orbits in right triangles, deducing periodic billiard paths and classifying orbit closures.
We address the question of determining the eigenvalues (listed in nondecreasing order, with multiplicities) for which Courant's nodal domain theorem is sharp i.e., for which there exists an associated eigenfunction with nodal domains (Courant-sharp eigenvalues). Following ideas going back to Pleijel (1956), …
New Jordan Floer homology shows every curve inscribes every isosceles trapezoid.
Continuous curves inscribe isosceles trapezoids in complex plane.
Study constant mean curvature tori in R^3 using spectral data and Whitham deformations.
Characterizes billiard and quasigeodesic flows in polyhedral convex bodies.
We review the theory of intrinsic geometry of convex surfaces in the Euclidean space and prove the following theorem: if the surface of a convex body K contains arbitrary long closed simple geodesics, then K is an isosceles tetrahedron.
We examine a Type-1 neck pinch singularity in simplicial Ricci flow (SRF) for an axisymmetric piecewise flat 3-dimensional geometry with 3-sphere topology. SRF was recently introduced as an unstructured mesh formulation of Hamilton's Ricci flow (RF). It describes the RF of a piecewise-flat simplicial geometry. In this …
In this paper, we give a classification of all compact Hermitian manifolds with flat Bismut connection. We show that the torsion tensor of such a manifold must be parallel, thus the universal cover of such a manifold is a Lie group equipped with a bi-invariant metric and a compatible left invariant complex structure. I…
Napoleonic triangles don't exist in hyperbolic geometry.
New bounds on inscribed triangles in arbitrary planar domains.
Paper calculates eigenvalues of a specific triangle on a sphere.
New method shows any triangle group generating pair is related to special coverings.
Complex hyperbolic triangle groups were first considered by Mostow in building the first nonarithmetic lattices in PU(2, 1). They are a natural generalization of the classical triangle groups acting on the hyperbolic plane. A well-known theorem of Takeuchi is that there are only finitely many Fuchsian triangle groups t…
Defines band maps in unoriented link Floer homology forming a skein exact triangle.
Proves a new skein exact triangle for real monopole Floer homology.
New surgery exact triangles in Heegaard Floer homology for rational slopes.
We answer the question "Does the Y-triangle move preserve intrinsic knottedness?" in the negative by giving an example of a graph that is obtained from the intrinsically knotted graph K_7 by triangle-Y and Y-triangle moves but is not intrinsically knotted.
Study calculates eigenvalues and eigenfunctions for spherical triangles and finds fundamental gap behavior.
We show that the triangle with angles Pi/12, Pi/3 and 7*Pi/12 has the lattice property and compute this triangle's Veech group.
We study side-lengths of triangles in path metric spaces. We prove that unless such a space X is bounded, or quasi-isometric to line or half-line, every triple of real numbers satisfying the strict triangle inequalities, is realized by the side-lengths of a triangle in X. We construct an example of a complete path metr…
Two triples of triangles having pairwise disjoint outlines in 3-space are called combinatorially isotopic if one triple can be obtained from the other by a continuous motion during which the outlines of the triangles remain pairwise disjoint. We conjecture that it can be algorithmically checked if an (ordered or unorde…
New method proves mateability of triangle groups with Blaschke products.
In this paper we study the area of ideals triangles in a convex domain with its Hilbert geometry. We obtain a characterization of the hyperbolic geometry among all the Hilbert geometry in terms of area of ideals triangles. We also obtain a sharp lower bound on the hilbert area of ideal triangles, independant of the con…
In Lorentzian geometry, limited definition of angles restricts the use of angle bisectors in study of triangles. This paper redefines angle bisectors so that they can be used to study attributes of triangles. Using the new definition, this paper investigates the existence of the incenter and the isogonal conjugate of a…
A formula for Rademacher symbols in triangle groups is provided.
Study stabilizers of complex hyperbolic triangle groups, finding generators and signatures.
Criterion for stopping conjugacy class enumeration in triangle groups.
New skein exact triangles for link Floer homology.
New theorem disproves Angle Defect for super triangles.
The study examines Lipschitz normally embedded Hölder triangles in 4D space.
Triangle Artin groups split as graphs of free groups under specific conditions.
The paper finds extremum values for mixed Laplacian eigenvalues on triangles and trapezoids.
Study on 3D surfaces and tangles formed by Poncelet triangles.
Study of subgroups in complex hyperbolic lattice triangle groups.
Triangle groups uniquely identified by their finite quotients.
Paper shows any link can be diagrammed with only triangles and quadrilaterals.
Given a closed polygon P having n edges, embedded in R^d, we give upper and lower bounds for the minimal number of triangles t needed to form a triangulated PL surface in R^d having P as its geometric boundary. The most interesting case is dimension 3, where the polygon may be knotted. We use the Seifert suface constru…
The paper extends Menelaus' and Ceva's theorems to translation triangles in various Thurston geometries.
We study groups generated by three half-turns in the Lobachevsky -space and their quotient orbifolds. These generalized triangle groups are closely related to the arbitrary 2-generator Kleinian groups. Our main result is a classification of the singular sets of the generalized triangle orbifolds. We also present a m…
Study on Teichmüller space of acute triangles using explicit calculations.
Identifies Anosov representations of hyperbolic triangle groups in SL(3,R).
We classify the 3-dimensional hyperbolic polyhedral orbifolds that contain no embedded essential 2-suborbifolds, up to decomposition along embedded hyperbolic triangle orbifolds (turnovers). We give a necessary condition for a 3-dimensional hyperbolic polyhedral orbifold to contain an immersed (singular) hyperbolic tur…
We consider the Neumann Laplacian acting on square-integrable functions on a triangle in the hyperbolic plane that has one cusp. We show that the generic such triangle has no eigenvalues embedded in its continuous spectrum. To prove this result we study the behavior of the real-analytic eigenvalue branches of a degener…
In this paper we mainly pay attention to the complex hyperbolic triangle groups of type (m, n, infinity) and discuss the discreteness. From the results more explicit conclusions about the triangle groups of type (n, infinity, infinity) will also be given.
Describes the space of spherical triangles on a smooth 3-manifold.