Projects / Programmes
January 1, 2009
- December 31, 2014
| Code |
Science |
Field |
Subfield |
| 1.01.00 |
Natural sciences and mathematics |
Mathematics |
|
| Code |
Science |
Field |
| P130 |
Natural sciences and mathematics |
Functions, differential equations |
| Code |
Science |
Field |
| 1.01 |
Natural Sciences |
Mathematics |
Stein manifolds, holomorphic maps, complex manifolds, proper maps, Stein domains, complex points, strictly pseudoconvexconvex hypersurfaces, plurisubharmonic functions, argument principle, h-principle, analytic extensions, integrable systems, isometries of Banach spaces, Riesz transforms.
Researchers (23)
Organisations (2)
Abstract
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
Significance for science
Work on this research led to important original scientific discoveries in the field of complex analysis and geometry, minimal surfaces, harmonic analysis, partial differential equations, andintegrable systems. The results were properly explained in detail, and documented through publications in international scientific journals with impact factor. Main results were also disseminated through numerous invited lectures at international conferences, including some high level plenary lectures, through course at several international PhD schools, and by lectures at foreign Universities and research institutions. The results achieved in the scope of this program gained international recognition as can be seen by citations, and also by numerous invitations to present these results at international conferences and foreign research institutions. The publication of a scientific monograph, author by F. Forstneric, by Springer-Verlag in August 2011, led to a wider visibility and accessibility of our research achievements, in particular among younger generations of researchers worldwide.
Significance for the country
Our scientific achievements compare rather favorably with those of leading research groups in our field, both in Europe and worldwide. For this reason our research work substantially contributed to the international visibility and recognition of Slovenia in the field ofmathematical sciences. The new knowledge that was achieved through work on this program was continuously used and transferred to our working environment, mainly through lectures at all levels of studies at the University of Ljubljana, but also through organization of scientific seminars, visits of foreign experts and lecturers, organization of research conferences both at home and abroad, etc. Through these and other activities we are continuously striving to create stimulating environment for the ripening of new ideas, and for the education and development of new generations of engineers, teachers, professor and researchers. When necessary and appropriate, we also actively participate in social aspects of the development and maintenance of education and science, in particular by expressing opinions in occasionally also by taking on leading roles and positions in our institutions. Through our editorial work at domestic and international journals we substantially contribute to the development and progress in education and science, both in Slovenia and worldwide.
Audiovisual sources (1)
| no. |
Title (with video link) |
Event |
Source |
| 1. |
Analysis and geometry |
Promotional video of research programme on Videolectures |
Research programme video presentation
|
Most important scientific results
Annual report
2009,
2010,
2011,
2012,
2013,
final report,
complete report on dLib.si
Most important socioeconomically and culturally relevant results
Annual report
2009,
2010,
2011,
2012,
2013,
final report,
complete report on dLib.si
