Advances in Mathematical Analysis with Applications

Dear Colleagues,

Cauchy–Riemann (C-R) analysis is the study of properties of solutions to the tangential C-R equations f = 0 on the boundary of a domain Ω ⊂ Cⁿ, which originates in the complex analysis of functions of several complex variables and sets at work methods in subelliptic theory (vis-à-vis Hörmander systems of vector fields locally associated with f = 0) and differential geometry (due to the recast of f = 0 as a CR structure).

Contributions are sought on the following themes:

    1) CR extension problem;

    2) CR embedding problem;

    3) Subelliptic harmonic maps;

    4) Fefferman's metric and space-time physics;

    5) Shear free null geodesic congruences on  Lorentzian manifolds;

    6) Spectral geometry for the sub-Laplacian on a CR manifold;

    7) CR immersions and the CR rigidity problem;

    8) Dirac equations on CR manifolds;

    9) Solvability of a Lewy operator and knot topology.

Dr. Elisabetta Barletta
Guest Editor

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• tangential cauchy–riemann equations
• hörmander system
• CR extension problem
• CR embedding problem
• subelliptic harmonic map
• Fefferman metric
• sub-Laplacian
• CR immersion
• Dirac equation
• Lewy operator