Analysis and geometry
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We intend to perform research and obtain new results in thirteen areas in complex analysis and geometry, global analysis, functional analysis and geometry, and harmonic analysis. These areas are:
1. Complex analysis and geometry
- Study of nonlinear boundary value problems for quazilinear equations on finite Riemann surfaces
- Construction of proper holomorphic maps from the disc whose ranges miss a given pluripolar set
- Construction of regular holomorphic maps from Stein manifolds to complex manifolds
- Construction of differentiable Cauchy-Riemann embeddings of strictly pseudoconvex hypersurfaces into spheres
- Construction of Stein domains in non-Stein complex manifolds
- Analysis of complex analytic properties of real surfaces embedded into complex surfaces
- Morse theory of plurisubharmonic functions
- Boundaries of analytic sets and the argument principle
- H-principle for modified Stein Spaces
- Analytic extensions from families of curves
2. Global analysis
- Singularity structure of integrable systems
3. Functional analysis and geometry
- Isometries of Banach spaces and special norms on finite-dimensional spaces
4. Harmonic analysis
- Riesz transforms
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