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.
Introduces a new -Hilbert functional in -geometry.
Global inverse function theorem proved easily using Riemannian geometry.
Bi-forms extend contrast functions to handle torsion in information geometry.
Regularizers change the geometric properties of loss functions in neural networks.
We find analogues of the Willmore functional for each of the Thurston geometries with 4-dimensional isometry group such that the CMC-spheres in these geometries are critical points of these functionals.
This study connects ReLU neural networks to toric geometry to analyze function realization.
Developed a theory of ultradifferentiable sheafs with applications.
The paper uses complex-valued functions to simplify plane differential geometry and kinematics.
PINNs solve differential geometry problems in complex shapes.
Study connects hyperbolic geometry to membrane shapes.
Link between Teichmüller and anti de Sitter geometry via length functions.
The paper extends the functional geometry of the visual cortex to more complex architectures using contactization and symplectization.
Global existence and geometry of constant mass aspect function foliation in perturbed Schwarzschild spacetime studied.
Lagrange geometry is the geometry of the tensor field defined by the fiberwise Hessian of a non degenerate Lagrangian function on the total space of a tangent bundle. Finsler geometry is the geometrically most interesting case of Lagrange geometry. In this paper we study a generalization, which consists of replacing th…
Defines metrics and Einstein tensors on Riemannian manifolds, proving vanishing for non-commutative two-torus.
We provide some examples of harmonic unit vector fields as normalized gradients of isoparametric functions from a K-contact geometry setting.
Algebraic geometry replaces manifolds in differential geometry.
Diffeologies unify infinite-dimensional geometry and PDEs, enhancing classical function spaces.
We construct new explicit proper biharmonic functions on the -dimensional Thurston geometries $\Sol$, $\Nil$, $\SL2$, $H^2\times\rn$ and $S^2\times\rn$.
Study distance functions on manifolds linking geometry to topology.
Study the geometry of bifurcation sets for specific types of functions.
It is shown that Electromagnetism creates geometry different from Riemannian geometry. General geometry including Riemannian geometry as a special case is constructed. It is proven that the most simplest special case of General Geometry is geometry underlying Electromagnetism. Action for electromagnetic field and Maxwe…
We derive a class of variational functionals which arise naturally in conformal geometry. In the special case when the Riemannian manifold is locally conformal flat, the functional coincides with the well studied functional which is the integration over the manifold of the k-symmetric function of the Schouten tensor of…
In this paper we introduce and study the notion of plurisubharmonic functions in calibrated geometry. These functions generalize the classical plurisubharmonic functions from complex geometry and enjoy many of their important properties. Moreover, they exist in abundance whereas the corresponding pluriharmonics are gen…
New method aligns brain data across individuals for better brain decoding.
The goal of this paper is to encode equivalently the fractional Lagrange dynamics as a nonholonomic almost Kahler geometry. We use the fractional Caputo derivative generalized for nontrivial nonlinear connections (N-connections) originally introduced in Finsler geometry, with further developments in Lagrange and Hamilt…
We characterize functions which are growth types of Riemannian manifolds of bounded geometry.
Extends Riemannian geometry inequalities with sharper estimates.
For any positive natural number we construct new explicit proper -harmonic functions on the celebrated -dimensional Thurston geometries $\Sol$, $\Nil$, $\SL2$, $\H^2\times\rn$ and $\s^2\times\rn$.
This article provides a brief discussion of the functional of super Riemann surfaces from the point of view of classical (i.e. not "super-) differential geometry. The discussion is based on symmetry considerations and aims to clarify the "borderline" between classical and super differential geometry with respect to the…
New classification of Kähler-Ricci solitons linked to isoparametric functions and contact geometry.
A method to generalize results from Riemannian Geometry to Finsler geometry is presented. We use the method to generalize several results that involve only metric conditions. Between them we show that the topology induced by the Finsler structure is equivalent to the manifold topology, we provide a new proof of the Hop…
A function is exponentially concave if its exponential is concave. We consider exponentially concave functions on the unit simplex. In a previous paper we showed that gradient maps of exponentially concave functions provide solutions to a Monge-Kantorovich optimal transport problem and give a better gradient approximat…
We review the complex differential geometry of the space of oriented affine lines in and give a description of Hamilton's characteristic functions for reflection in an oriented C surface in terms of this geometry.
Convexity and convex functions play an important role in theoretical physics. To initiate a study of the possible uses of convex functions in General Relativity, we discuss the consequences of a spacetime or an initial data set admitting a suitably defined convex function. We show how…
Convexity and convex functions play an important role in theoretical physics. To initiate a study of the possible uses of convex functions in General Relativity, we discuss the consequences of a spacetime or an initial data set admitting a suitably defined convex function. We show how…
Studying various functionals and associated gradient ows are known problems in differential geometry. The perpose of this article is to provide a general overview of curvature functionals in Finsler geometry and use their information for introducing different gradient ows on Finsler manifolds.
We determine when an arithmetic subgroup of a reductive group defined over a global function field is of type FP_\infty by comparing its large-scale geometry to the large-scale geometry of lattices in real semisimple Lie groups.
Algebras of generalized functions offer possibilities beyond the purely distributional approach in modelling singular quantities in non-smooth differential geometry. This article presents an introductory survey of recent developments in this field and highlights some applications in mathematical physics.
We describe some general constructions on a real smooth projective 4-quadric which provide analogues of the Willmore functional and conformal Gauss map in both Lie sphere and projective differential geometry. Extrema of these functionals are characterized by harmonicity of this Gauss map.
The following is a compilation of some techniques in Alexandrov's geometry which are directly connected to convexity.
The paper explores the geometry of the Spence-Kummer trilogarithm equation and its Galois analogue.
The paper defines function spaces on manifolds with bounded or singular geometries.
We introduce and study the notion of plurisubharmonic functions in calibrated geometry. These functions generalize the classical plurisubharmonic functions from complex geometry and enjoy their important properties. Moreover, they exist in abundance whereas the corresponding pluriharmonics are generally quite scarce. A…
Develops a new algebraic framework for differential geometry of infinite dimensional spaces.
The study extends calibrated geometry to smooth maps and finds energy bounds.
New proof of four squares theorem using projective geometry.
Fundamental solutions found for PDEs in Finsler geometry.