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.
PPO-B improves sampling efficiency by using a logarithmic barrier method.
Method learns Dirichlet-to-Neumann maps on graphs using Gaussian processes.
Study exterior maximal surfaces with precise asymptotic behavior.
Classifies essential annuli in a genus two handlebody exterior.
The paper classifies symmetries and determines exterior types of knotted handlebodies.
We give a topological characterisation of alternating knot exteriors based on the presence of special spanning surfaces. This shows that alternating is a topological property of the knot exterior and not just a property of diagrams, answering an old question of Fox. We also give a characterisation of alternating link e…
The study classifies area-maximizing hypersurfaces with singularities and exterior domains.
Discrete exterior calculus shows natural properties of wedge product and averaging.
The study finds infinite knot exteriors with meridional surfaces of any genus and boundary components.
A brief introduction to exterior differential systems for graduate students familiar with manifolds and differential forms. For complete files, see https://github.com/Ben-McKay/introduction-to-exterior-differential-systems
Extends exterior diff. sys. to Lie algebroids with examples.
The study finds infinite meridional essential surfaces in hyperbolic knot exteriors of various genera.
Algorithm finds knot diagrams from exterior triangulations.
It is shown that two definitions for an exterior differential in superspace, giving the same exterior calculus, yet lead to different results when applied to the Poisson bracket. A prescription for the transition with the help of these exterior differentials from the given Poisson bracket of definite Grassmann parity t…
Evolutionary forms, as well as exterior forms, are skew-symmetric differential forms. But in contrast to the exterior forms, the basis of evolutionary forms is deforming manifolds (with unclosed metric forms). Such forms possess a peculiarity, namely, the closed inexact exterior forms are obtained from that. The closur…
Paper introduces an invariant to distinguish handlebody-knot exteriors.
A new discrete calculus for bundle-valued forms is proposed and validated.
Thurston's Circle Pattern Theorem studies existence and rigidity of circle patterns of a given combinatorial type and the given non-obtuse exterior intersection angles. Using topological degree theory, variational principle, Teichmuller theory, and Sard's Theorem, this paper generalizes Circle Pattern Theorem to the ca…
We give a characterization of alternating link exteriors in terms of cubed complexes. To this end, we introduce the concept of a "signed BW cubed-complex", and give a characterization for a signed BW cubed-complex to have the underlying space which is homeomorphic to an alternating link exterior.
Paper shows non-convexity in solutions to Hessian equations.
Extends Minkowski stability proof to minimal decay assumptions.
A generalization of exterior calculus is considered by allowing the partial derivatives in the exterior derivative to assume fractional orders. That is, a fractional exterior derivative is defined. This is found to generate new vector spaces of finite and infinite dimension, fractional differential form spaces. The def…
Study of group orderability using tensor and exterior squares.
We give an elegant formulation of the structure equations (of Cartan) and the Bianchi identities in terms of exterior calculus without reference to a particular basis and without the exterior covariant derivative. This approach allows both structure equations and the Bianchi identities to be expressed in terms of forms…
New disks found with similar outer shapes.
Paper solves overdetermined -Hessian equation in exterior domains.
Maxwell meets Korn: A New Coercive Inequality for Tensor Fields with Square-Integrable Exterior Derivative
Survey revisits vector calculus results using exterior derivative and provides a new formulation of Stokes' theorem.
Exterior differential systems are given, and their Cartan characters calculated, for Maxwell and SU(2)-Yang-Mills equations in dimensions from three to six.
Extends Young integral to Hölder differential forms in arbitrary dimensions.
The Whitehead link exterior lacks most Euler class taut foliations.
We study in detail Hodge-Helmholtz decompositions in non-smooth exterior domains filled with inhomogeneous and anisotropic media. We show decompositions of alternating differential forms belonging to weighted Sobolev spaces into irrotational and solenoidal forms. These decompositions are essential tools, for example, i…
We construct a two-parameter covariant differential calculus on the quantum -exterior plane. We also give a deformation of the two-dimensional fermionic phase space.
The paper explores nonconvex penalties for deep learning regularization.
Researchers prove constant mean curvature graphs in hyperbolic 3-space for specific domains.
Brunnian theta curves in 3D spheres have hyperbolic exteriors.
We provide a classification of the essential surfaces of non-negative Euler characteristic in the exteriors of genus two handlebodies embedded in the 3-sphere.
I describe work in progress with Baryshnikov and Zharnitsky on periodic billiard orbits that leads one to an exterior differential system (EDS). I then give a brief introduction to EDS illustrated by several examples.
Operational guide to discrete exterior calculus on cubic cells.
Geometrically reformulates elasticity theory using exterior calculus.
Abstract: Study Kähler identities on almost complex manifolds.
In this paper, we show that, for each non-trivial two bridge knot K and for each g > 2, every genus g Heegaard splitting of the exterior E(K) of K is reducible.
This is an elementary introduction to exterior differential systems motivated by two examples: minimal submanifolds and the isometric embedding problem. The two main goals of the lectures are: 1. To explain how to find an appropriate geometric setting for studying a given system of pde. 2. To explain the Cartan algorit…
The paper generalizes Monge-Ampère equations and their solutions in differential geometry.
We show that a handlebody-knot whose exterior is boundary-irreducible has a unique maximal unnested set of knotted handle decomposing spheres up to isotopies and annulus-moves. As an application, we show that the handlebody-knots and are not equivalent. We also show that some genus two handlebody-knot…
This paper describes the algorithms, features and implementation of PyDEC, a Python library for computations related to the discretization of exterior calculus. PyDEC facilitates inquiry into both physical problems on manifolds as well as purely topological problems on abstract complexes. We describe efficient algorith…
Proves stability of Minkowski space-time for Einstein-Yang-Mills equations.
We study the intrinsic torsion of almost quaternion-Hermitian manifolds via the exterior algebra. In particular, we show how it is determined by particular three-forms formed from simple combinations of the exterior derivatives of the local Kaehler forms. This gives a practical method to compute the intrinsic torsion a…