Malé množiny v prostorech křivek a ploch
| Thesis title in Czech: | Malé množiny v prostorech křivek a ploch |
|---|---|
| Thesis title in English: | Small sets in spaces of curves and surfaces |
| Key words: | rektifikovatelná množina, extremální délka, geometrická teorie míry, prostory slabě diferencovatelných funkcí |
| English key words: | rectifiable set, extremal length, geometric measure theory, spaces of weakly differentiable functions |
| Academic year of topic announcement: | 2011/2012 |
| Thesis type: | dissertation |
| Thesis language: | angličtina |
| Department: | Department of Mathematical Analysis (32-KMA) |
| Supervisor: | prof. RNDr. Stanislav Hencl, Ph.D. |
| Author: | hidden - assigned and confirmed by the Study Dept. |
| Date of registration: | 26.09.2011 |
| Date of assignment: | 26.09.2011 |
| Confirmed by Study dept. on: | 02.11.2011 |
| Guidelines |
| Studovat malé množiny v prostorech křivek a ploch na základě metody "extremální délky", kterou na základě myšlenky A. Beurlinga a L. Ahlforse rozpracoval B. Fuglede.
Zkoumat možnost aplikace na geometrickou teorii míry, stopy slabě diferencovatelných zobrazení, integrace vzhledem k distribucím. |
| References |
| H. Federer: Geometric measure theory. Springer-Verlag New York Inc., New York 1969.
B. Fuglede: Extremal length and functional completion. Acta Math. 98 1957 171–219. G. A. Leoni: A first course in Sobolev spaces. Graduate Studies in Mathematics, 105. American Mathematical Society, Providence, RI, 2009. J. Väisälä: Lectures on n-dimensional quasiconformal mappings. Lecture Notes in Mathematics 229. Springer-Verlag, Berlin-New York, 1971. H. Whitney: Geometric integration theory. Princeton University Press, Princeton, 1957 |
| Preliminary scope of work |
| Výjimečné množiny v prostorech křivek a ploch ve smyslu Fugledeovy teorie. |
| Preliminary scope of work in English |
| Exceptional sets in spaces of curves and surfaces in terms of Fuglede's theory |