Gabriel P. Paternain

1. The boundary rigidity problem in the presence of a magnetic field
   2006/11/25 by N. S. Dairbekov, Gabriel P. Paternain, Dairbekov, N. S. +5 · 4 citations
   Computer Science · Mathematics · #Advanced Mathematical Modeling in Engineering #Analysis of PDEs (math.AP) #Differential Geometry (math.DG) #FOS: Mathematics #Nonlinear Partial Differential Equations #Numerical methods in inverse problems
2. Invariant distributions, Beurling transforms and tensor tomography in higher dimensions
   2015/01/31 by Gabriel P. Paternain, Mikko Salo, Günther Uhlmann +1 · 5 citations
   Physics and Astronomy · Mathematics · #Advanced Differential Geometry Research #Mathematical Analysis and Transform Methods #Geometric Analysis and Curvature Flows
3. The X-Ray Transform for Connections in Negative Curvature
   2015/11/23 by Colin Guillarmou, Gabriel P. Paternain, Mikko Salo +2 · 4 citations
   Mathematics · Engineering · #Numerical methods in inverse problems #Thermoelastic and Magnetoelastic Phenomena #Geometric Analysis and Curvature Flows
4. Rigidity properties of Anosov optical hypersurfaces
   2005/08/17 by Nurlan S. Dairbekov, N. S. Dairbekov, Gabriel P. Paternain +2 · 2 citations
   Mathematics · #Geometric Analysis and Curvature Flows #Geometric and Algebraic Topology #Mathematical Dynamics and Fractals #math.DG #math.DS
5. Detection of Hermitian connections in wave equations with cubic non-linearity
   2019/02/15 by Xi Chen, Chen, Xi, Matti Lassas +5 · 4 citations
   Earth and Planetary Sciences · Mathematics · #35R30 #Analysis of PDEs (math.AP) #FOS: Mathematics #FOS: Physical sciences #Mathematical Analysis and Transform Methods #Mathematical Physics (math-ph) #Numerical methods in inverse problems #Seismic Imaging and Inversion Techniques
6. Statistical guarantees for Bayesian uncertainty quantification in non-linear inverse problems with Gaussian process priors
   2020/07/31 by François Monard, Richard Nickl, Monard, François +3 · 4 citations
   Computer Science · Decision Sciences · Engineering · #Gaussian Processes and Bayesian Inference #Scientific Measurement and Uncertainty Evaluation #Reservoir Engineering and Simulation Methods
7. On some information-theoretic aspects of non-linear statistical inverse problems
   2021/07/20 by Richard Nickl, Nickl, Richard, Gabriel P. Paternain +1 · 3 citations
   Computer Science · Mathematics · #Bayesian Methods and Mixture Models #FOS: Mathematics #Gaussian Processes and Bayesian Inference #Statistical Methods and Inference #Statistics Theory (math.ST)
8. Broken ray tensor tomography with one reflecting obstacle
   2018/05/13 by Joonas Ilmavirta, Ilmavirta, Joonas, Gabriel P. Paternain +1 · 2 citations
   Engineering · Mathematics · Medicine · #44A12 #53A35 #58C99 #58J90 #Analysis of PDEs (math.AP) #Differential Geometry (math.DG) #Elasticity and Material Modeling #FOS: Mathematics #Geometric Analysis and Curvature Flows #Medical Imaging Techniques and Applications
9. Boundary rigidity for Lagrangian submanifolds, non-removable intersections, and Aubry-Mather theory
   2002/07/17 by Gabriel P. Paternain, Paternain, Gabriel P., Leonid Polterovich +3 · 1 citation
   Mathematics · #Dynamical Systems (math.DS) #FOS: Mathematics #Geometric Analysis and Curvature Flows #Geometric and Algebraic Topology #Geometry and complex manifolds #Symplectic Geometry (math.SG) #math.DS #math.SG
10. Zero entropy and bounded topology
    2004/06/02 by Gabriel P. Paternain, Jimmy Petean, Paternain, Gabriel P. +1 · 1 citation
    Computer Science · Mathematics · #Geometric Analysis and Curvature Flows #Homotopy and Cohomology in Algebraic Topology #Topological and Geometric Data Analysis #math.DG #math.DS
11. Dynamically convex Finsler metrics and J-holomorphic embedding of asymptotic cylinders
    2007/01/22 by Adam Harris, Harris, Adam, Gabriel P. Paternain +1 · 1 citation
    Mathematics · Physics and Astronomy · #Advanced Differential Geometry Research #Differential Geometry (math.DG) #FOS: Mathematics #Geometric Analysis and Curvature Flows #Symplectic Geometry (math.SG)
12. On the injectivity of the X-ray transform for Anosov thermostats
    2007/08/07 by Dan Jane, Gabriel P. Paternain, Jane, Dan +1 · 1 citation
    Computer Science · Mathematics · Physics and Astronomy · #Dynamical Systems (math.DS) #FOS: Mathematics #Statistical Mechanics and Entropy #Topological and Geometric Data Analysis #advanced mathematical theories
13. On the stability of Mañé critical hypersurfaces
    2009/10/29 by Leonardo Macarini, Macarini, Leonardo, Gabriel P. Paternain +1 · 1 citation
    Mathematics · Physics and Astronomy · #Advanced Differential Equations and Dynamical Systems #Dynamical Systems (math.DS) #FOS: Mathematics #Geometry and complex manifolds #Nonlinear Waves and Solitons #Symplectic Geometry (math.SG)
14. On the range of the attenuated ray transform for unitary connections
    2013/02/20 by Gabriel P. Paternain, Mikko Salo, Paternain, Gabriel P. +3 · 2 citations
    Physics and Astronomy · Mathematics · Engineering · #Advanced Differential Geometry Research #Mathematical Analysis and Transform Methods #Advanced Numerical Analysis Techniques
15. Tensor tomography: progress and challenges
    2013/03/25 by Gabriel P. Paternain, Mikko Salo, Paternain, Gabriel P. +3 · 1 citation
    Physics and Astronomy · #Black Holes and Theoretical Physics #Cosmology and Gravitation Theories #Noncommutative and Quantum Gravity Theories
16. On the interplay between the light ray and the magnetic X-ray transforms
    2025/02/06 by Lauri Oksanen, Gabriel P. Paternain, Oksanen, Lauri +3 · 4 citations
    Engineering · Physics and Astronomy · #35R30 #53C50 #53C65 #Analysis of PDEs (math.AP) #Differential Geometry (math.DG) #Experimental and Theoretical Physics Studies #FOS: Mathematics #FOS: Physical sciences #General Relativity and Quantum Cosmology (gr-qc) #Geophysics and Sensor Technology #Radioactive Decay and Measurement Techniques
17. A sharp stability estimate for tensor tomography in non-positive\n curvature
    2020/01/13 by Gabriel P. Paternain, Mikko Salo, Paternain, Gabriel P. +1 · 1 citation
    Computer Science · Mathematics · #Advanced Mathematical Modeling in Engineering #Analysis of PDEs (math.AP) #Differential Geometry (math.DG) #FOS: Mathematics #Mathematical Analysis and Transform Methods #Numerical methods in inverse problems
18. The non-Abelian X-ray transform on surfaces
    2020/06/03 by Gabriel P. Paternain, Paternain, Gabriel P., Mikko Salo +1 · 1 citation
    Mathematics · #Algebraic and Geometric Analysis #Analysis of PDEs (math.AP) #Differential Geometry (math.DG) #FOS: Mathematics #Mathematical Analysis and Transform Methods #advanced mathematical theories
19. Resonant forms at zero for dissipative Anosov flows
    2022/11/11 by Mihajlo Cekić, Gabriel P. Paternain, Cekić, Mihajlo +1 · 1 citation
    Mathematics · #Mathematical Dynamics and Fractals #Geometry and complex manifolds #Geometric and Algebraic Topology