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arXiv research

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.

168,657 papers · 148 categories

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5 results for “0-calculus”

Boundary value problems for 0-elliptic operatorsmath.AP

New calculus solves boundary value problems for elliptic operators.

problem Boundary value problems for 0-elliptic operators.

method Developed a new calculus called symbolic 0-calculus to handle boundary value problems.

result Construct left and right parametrices for 0-elliptic operators with boundary conditions.

Boundary value problems 0-elliptic operators Pseudodifferential operators Symbolic calculus Elliptic boundary conditions

2024-12-08abs ↗pdf ↗

Einstein-Yang-Mills fields in conformally compact manifoldsmath.DG

Study Einstein-Yang-Mills fields on specific manifolds, proving field deformations.

problem Deforming Einstein-Yang-Mills fields over conformally compact manifolds.

method Deformation theory using

0

-calculus of Mazzeo and Melrose.

result Any small perturbation of boundary data can be realized as an Einstein-Yang-Mills field.

Einstein-Yang-Mills fields conformally compact manifolds deformation theory 0-calculus Poincaré-Einstein

2023-04-11abs ↗pdf ↗

Dirichlet-to-Neumann Map for Poincaré-Einstein Metrics in Even Dimensionsmath.DG

We study the linearization of the Dirichlet-to-Neumann map for Poincaré-Einstein metrics in even dimensions on an arbitrary compact manifold with boundary. By fixing a suitable gauge, we make the linearized Einstein equation elliptic. In this gauge the linearization of the Dirichlet-to-Neumann map appears as the scatte…

2009-05-15abs ↗pdf ↗

Self-adjointness criteria and self-adjoint extensions of the Laplace-Beltrami operator on

α

-Grushin manifoldsmath.DG

The paper explores self-adjointness of Laplace-Beltrami operator on special geometric manifolds.

problem Characterizing self-adjoint extensions of the Laplace-Beltrami operator on

α

-Grushin manifolds.

method Introducing an exotic calculus of pseudodifferential operators adapted to the geometry of the singularity.

result Criterion for essential self-adjointness and determination of several self-adjoint extensions.

Grushin plane sub-Riemannian geometry spectral theory pseudo-differential operators Laplace-Beltrami operator

2023-05-14abs ↗pdf ↗

Tensor tomography on asymptotically hyperbolic surfacesmath.DG

Study geodesic X-ray transforms on hyperbolic surfaces, proposing new reconstruction methods.

problem Inverting geodesic X-ray transforms for symmetric tensor fields on asymptotically hyperbolic surfaces.

method Developed a decomposition theorem for m-tensor fields, used Guillemin-Kazhdan operators and 0-calculus, and provided explicit reconstruction methods.

result Explicit reconstruction methods for even tensor fields from their X-ray transform or normal operator.

Tensor tomography Asymptotically hyperbolic surfaces Geodesic X-ray transform Symmetric tensor fields Iterated-tt form

2025-10-05abs ↗pdf ↗