Geometric Analysis and Mathematical Physics
A special issue of Axioms (ISSN 2075-1680). This special issue belongs to the section "Mathematical Physics".
Deadline for manuscript submissions: closed (20 December 2019) | Viewed by 12803
Special Issue Editor
Interests: nonlinear PDEs systems of variational origin, e.g., harmonic map system; Bergman kernels; tangential Cauchy–Riemann equations; Lorentzian geometry; general relativity and gravitation theory
Special Issue Information
Dear Colleagues,
This Special Issue Geometric Analysis and Mathematical Physics seeks to gather contributions by experts in
1) The theory of singularities of space-times, e.g., boundary constructions and singular holonomy, with applications to black hole mathematical physics;
2) Shearfree null geodesic congruences associated with Petrov type D solutions to gravitational field equations and a mathematical analysis of tangential Cauchy–Riemann equations, with applications to gravity coupled with electromagnetism, neutrino, and Dirac equations;
3) Fermat principles and variational theory of light rays versus the variational theory of Cartan–Chern–Moser chains, with applications to gravitational lensing and neutrino trapping;
4) The boundary behaviour of massive scalar particles building on the theory of reproducing kernel Hilbert spaces theory within the quantization of mechanical systems whose phase space is a Hermitian manifold.
Contributions seeking to unify gravity with other forces in nature (e.g., the coupling of gravity with sigma models) are welcome, as well as results from other areas of mathematical physics not comprised in the themes listed above.
The common feature of contributions, which lies at the heart of the volume to be realised, should be the mathematical rigour of methods belonging to differential geometry, both real and complex (curvature and characteristic classes, theory of G-structures, foliation theory, and Satake-Thurston orbifolds), to existence and regularity theory for solutions to partial differential equations — especially subelliptic as well suited to the study of the theory of Hörmander systems of vector fields, of Cauchy–Riemann geometry, and of Webster’s pseudohermitian geometry - harmonic maps and morphisms theory, and hence methods of complex analysis (of functions of one or several complex variables), of functional analysis, and harmonic analysis.
Prof. Dr. Sorin Dragomir
Guest Editor
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Keywords
- Tangential Cauchy–Riemann equations
- Lorentzian metric
- Killing vector field
- CR structure
- Tanaka–Webster connection
- Graham–Lee connection
- Fefferman metric
- Monge-Ampère equation
- Reproducing kernel Hilbert space
- Weighted kernel
- Dirac equation
- Harmonic map
- Cartan chain
- Orbifold
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