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Analysis and geometry

Analysis and geometry

This video was recorded at PRO(MO)GRAM - predstavitveni filmi raziskovalnih programov / promotional videos of research programs. 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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