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.
Paper finds new criteria for conjugate points in fluid flows.
An explicit expression is obtained for the sectional curvature in the plane spanned by two stationary flows, cos(k, x) and cos(l, x). It is shown that for certain values of the wave vectors k and l the curvature becomes positive for alpha > alpha_0, where 0 < alpha_0 < 1 is of the order 1/k. This suggests that the flow…
In this article, we show how to embed the so-called CH2 equations into the geodesic flow of the Hdiv metric in 2D, which, itself, can be embedded in the incompressible Euler equation of a non compact Riemannian manifold. The method consists in embedding the incompressible Euler equation with a potential term coming fro…
The Grove-Searle theorem on 2d manifolds with 8 or less symmetry groups has positive Euler characteristic.
Li-Yau inequality applied to curves in 2D space.
Computes a new metric quantity Y(M) for Riemannian 2d-manifolds.
This paper explores vortices and harmonic flows on compact surfaces, using Hodge decomposition.
Study of null mean curvature flow on de Sitter lightcone, related to 2d-Ricci flow.
Study of flows with a single singular point on a 2D disk.
Forward-Euler fails for simulating Wasserstein gradient flows with KL divergence.
Euler's equations for a two-dimensional system can be written in Hamiltonian form, where the Poisson bracket is the Lie-Poisson bracket associated to the Lie algebra of divergence free vector fields. We show how to derive the Poisson brackets of 2d hydrodynamics of ideal fluids as a reduction from the one associated to…
New ancient solutions found for curvature flow in 2D.
This paper is devoted to obtain the one-dimensional group invariant solutions of the two-dimensional Ricci flow ((2D) Rf) equation. By classifying the orbits of the adjoint representation of the symmetry group on its Lie algebra, the optimal system of one-dimensional subalgebras of the ((2D) Rf) equation is obtained. F…
The paper introduces branched α-flows on surfaces with negative Euler characteristic and proves their long-term existence and convergence.
Derive bihamiltonian structure for rational reduction of 2D-Toda hierarchy
New steady Euler flows found on 3-sphere and Sasakian manifolds.
We present an avatar of the Euler obstruction to foliated structures on certain non-metric surfaces. This adumbrates (at least for the simplest 2D-configurations) that the standard mechanism---to the effect that the devil of algebra sometimes barricades the existence of angelic geometric structures (obstruction theory …
We solve Euler equations on graph manifolds, classifying steady flows with Morse-Bott Bernoulli functions.
Non-vanishing steady Euler flows and Beltrami fields found in high dimensions.
Existence of a conjugate point in the incompressible Euler flow on a sphere and an ellipsoid is considered. Misiolek (1996) formulated a differential-geometric criterion (we call M-criterion) for the existence of a conjugate point in a fluid flow. In this paper, it is shown that no zonal flow (stationary Euler flow) sa…
The study identifies unique fluid flow patterns.
A nontrivial smooth steady incompressible Euler flow in three dimensions with compact support is constructed. Another uncommon property of this solution is the dependence between the Bernoulli function and the pressure.
New perspective on Ricci flow on spheres using Minkowski spacetime.
We characterize, using commuting zero-flux homologies, those volume-preserving vector fields on a -manifold that are steady solutions of the Euler equations for some Riemannian metric. This result extends Sullivan's homological characterization of geodesible flows in the volume-preserving case. As an application, we…
Study how large-scale flows align small-scale vortices in 3D Euler equations.
Index expectation curvature K(x) = E[i_f(x)] on a compact Riemannian 2d-manifold M is the expectation of Poincare-Hopf indices i_f(x) and so satisfies the Gauss-Bonnet relation that the interval of K over M is Euler characteristic X(M). Unlike the Gauss-Bonnet-Chern integrand, such curvatures are in general non-local. …
In this note we first set up an analogy between spin and vorticity of a perfect 2d-fluid flow, based on the Borel-Weil contruction of the irreducible unitary representations of SU(2), and looking at the Madelung-Bohm velocity attached to the ensuing spin wave functions. We also show that, in the framework of finite dim…
In this article we construct a smooth Euler flow supported in a neighborhood of a helix. It may be considered a generalization of a similar solution found by the author for a circle.
We point out a duality between steady incompressible Euler flows and solutions of the strongly coupled Faddeev-Skyrme sigma model with potential (mass) term. We supplement this result with various applications and several explicit examples.
We develop an adversarial-reinforcement learning scheme for microswimmers in statistically homogeneous and isotropic turbulent fluid flows, in both two (2D) and three dimensions (3D). We show that this scheme allows microswimmers to find non-trivial paths, which enable them to reach a target on average in less time tha…
New model reconstructs flow from sparse data with uncertainty quantification.
Global minimizers exist for Tonelli Lagrangians on half-Lie groups.
New approach links 2D fluid dynamics to matrix theory.
New probabilistic constructions for Kähler-Einstein metrics.
The Euler class conjecture links geometric structures to integral points on the Thurston norm ball.
We discuss from a geometric point of view the connection between the renormalization group flow for non--linear sigma models and the Ricci flow. This offers new perspectives in providing a geometrical landscape for 2D quantum field theories. In particular we argue that the structure of Ricci flow singularities suggests…
In this paper we address several aspects of flat Bogomolnyi-Prasad-Sommerfeld (BPS) domain walls together with their Lorentz invariant vacua of 4d N=1 supergravity coupled to a chiral multiplet. The scalar field spans a one-parameter family of 2d Kähler manifolds satisfying a Kähler-Ricci flow equation. We find that BP…
We present a steady Euler flow on the round 3-sphere whose velocity vector field has the property of having two independent first integrals, being tangent to the fibres of an almost submersion onto the 2-sphere. This submersion turns out to be a critical point for the quartic Faddeev-Skyrme model with a standard potent…
EGFs use ergodicity to simplify generative flows for easier training and imitation learning.
Ancient flows by curvature powers in 2D have finite entropy.
A little complement concerning the dynamics of non-metric manifolds is provided, by showing that any flow on an -bounded surface with non-zero Euler character has a fixed point.
We analyze the Ricci flow of a noncompact metric that describes a two-dimensional black hole. We consider entanglement entropy of a 2d black hole which is due to the quantum correlations between two subsystems: one is inside and the other is outside the black hole horizon. It is demonstrated that the entanglement entro…
We prove a comparison theorem for the compact surfaces with negative Euler characteristic via the Ricci flow.
New proof confirms periodic orbit conjecture for Eulerisable flows.
In this paper, we present our general results about traversing flows on manifolds with boundary in the context of the flows on surfaces with boundary. We take advantage of the relative simplicity of -worlds to explain and popularize our approach to the Morse theory on smooth manifolds with boundary, in which the bo…
The paper explores the geometric properties of fluid flows and their symmetries.
Study of curve evolution in 2D space forms converging to a circle.
Straight lines are a basin of attraction for the elastic flow at least to level 1.9615π.