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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.

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6 results for “RT-equations”

Optimal Regularity and Uhlenbeck Compactness for General Relativity and Yang-Mills Theorygr-qc

Extends optimal regularity and Uhlenbeck compactness to non-Riemannian manifolds.

problem Establishing optimal regularity and compactness for connections on vector bundles over non-Riemannian manifolds.

method Proofs based on RT-equations for connections with

L^p

curvature, extending to non-compact gauge groups.

result Removes singularities at GR shock waves, ensuring existence of geodesics and coordinates.

Optimal Regularity Uhlenbeck Compactness General Relativity Yang-Mills Theory Non-Riemannian Manifolds

2022-02-19abs ↗pdf ↗

On the Optimal Regularity Implied by the Assumptions of Geometry II: Connections on Vector Bundlesmath.DG

Extends optimal regularity and compactness to vector bundles over non-Riemannian manifolds.

problem Optimal regularity and compactness for connections on vector bundles.

method Derive RT-equations, establish existence theory, handle curvature up to

L^1

result Optimal regularity and compactness extended to vector bundles over non-Riemannian manifolds.

connections vector bundles optimal regularity compactness RT-equations

2021-05-22abs ↗pdf ↗

The essential regularity of singular connections in geometrygr-qc

Paper finds essential regularity in singular connections.

problem Determining if singularities in connections are removable or essential.

method Introduces RT-equations and a procedure to lift connections to essential regularity.

result A computable procedure to lift connections to essential regularity.

singular connections essential regularity RT-equations L^p connections removable singularities

2024-12-12abs ↗pdf ↗

How to smooth a crinkled map of spacetime: Uhlenbeck compactness for

L^\infty

connections and optimal regularity for general relativistic shock waves by the Reintjes-Temple-equationsgr-qc

We present authors' new theory of the RT-equations, nonlinear elliptic partial differential equations which determine the coordinate transformations which smooth connections $Γ$ to optimal regularity, one derivative smoother than the Riemann curvature tensor ${\rm Riem}(Γ)$ . As one application we extend Uhlenbeck compa…

2018-12-14abs ↗pdf ↗

The Hawking Singularity Theorem for Hölder Continuous Metrics with

L^p

-Bounded Curvaturegr-qc

The paper extends Hawking's singularity theorem to metrics with Hölder continuity and bounded curvature.

problem Proving singularity theorems for metrics with low regularity.

method Combining elliptic RT-equations for metric regularisation and manifold convolution for curvature refinement.

result Establishes globally hyperbolic and timelike incompleteness for metrics with Hölder continuity and bounded curvature.

Hawking singularity theorem Lorentzian metrics W^{1 p}L^p-bounded curvature

2026-04-29abs ↗pdf ↗

Extreme Theory of Functional Connections: A Physics-Informed Neural Network Method for Solving Parametric Differential Equationscs.LG

X-TFC solves parametric DEs with neural networks and physics constraints.

problem Solving parametric differential equations with physics constraints.

method Combines Theory of Functional Connections and Physics-Informed Neural Networks with a single-layer Extreme Learning Machine.

result Achieves high accuracy with low computational time.

physics-informed neural networks functional connections parametric differential equations extreme learning machine neural networks

2020-05-15abs ↗pdf ↗