MSI3M · Minimal Surfaces in 3-manifolds
7РП — „Хора“ (Действия „Мария Кюри“)
- Период
- 2008-10-01 → 2012-09-30
- Финансиране от ЕС
- 100 000 €
- Участници
- 1
- Схема
- MC-IRG
Линиите свързват координатора с партньорите.
Накратко на български
Минималните повърхности в триизмерните пространства изследват геометрични форми с най-малка площ, като например формата на сапунен балон между две рамки. Тези анализи помагат за по-доброто разбиране на геометричната топология и диференциалната геометрия.
Кратко обяснение, генерирано от езиков модел по текста на CORDIS. Оригиналът е по-долу.
Резултати накратко
Minimal Surfaces in 3-manifolds
Dr Baris Coskunuzer, the researcher in charge of the project EU-FP7 IRG 226062 (acronym MSI3M), wishes to express his gratitude to the European Commission for their support on his research. Project objectives In this project, the principal investigator (PI) suggested to work on five problems in the fields of geometric topology and differential geometry. While some of the problems are very old, and any partial results would be an important contribution to the field, the others are very up-to-date, and close to the current interest. The problems are the following: 1. Embedded plateau problem; 2. Hyperbolic 3-manifolds with minimal foliation: 3. Universal cover problem; 4. Intersections of least area planes in hyperbolic space; 5. Properly embedded least area planes in hyperbolic 3-space. Work performed and main results The PI got substantial results on the problems mentioned above, and published these results in very respectable journals such as American Journal of Mathematics, International Mathematics Research Notices (IMRN), Transactions of the American Mathematical Society and Communications in Contemporary Mathematics. The PI had seven publications and two preprints during the project; the complete list is given in the publications section. You can reach the contents of the publications at the following webpage: http://home.ku.edu.tr/~bcoskunuzer. On the other hand, during this period, the PI was invited to give talks at many prestigious universities and conferences, such as Princeton University, Cambridge University, University of Texas at Austin, Yale University (detailed list given in Dissemination Activities section). Impact The PI was involved in many activities through organising, participating, and giving talks at various workshops and conferences in Turkey. He was invited to give talks at many prestigious universities and conferences in the EU and USA. Also, he hosted important researchers of the field in Turkey. He supervised four graduate students during the project. Via these activities, the PI has been able to transfer his knowledge and experience to Turkey and EU successfully. You can find the details of these activities in the Dissemination Activities section.
Текст от CORDIS, на английски · Данни: CORDIS, © Европейски съюз
Цел на проекта
Dr. Coskunuzer will undertake research in Differential Geometry and Geometric Topology. He will investigate the problems in minimal surface theory in hyperbolic space by using topological techniques. There are five main problems in the project. PROBLEM 1: (Universal Cover Conjecture) The first one is a famous classical 3-manifold topology problem, namely The Universal Cover Conjecture. The Conjecture asserts that the universal cover of any irreducible 3-manifold with infinite fundamental group is a 3-ball. This problem is one of the most famous problems in geometric topology. PROBLEM 2: (Intersections of Least Area Planes in Hyperbolic 3-space) The second main problem is about Least Area Planes in Hyperbolic 3-space. In recent years, Dr. Coskunuzer showed very strong generic uniqueness results on the subject. Now, he is studying the intersections of different least area planes with non-transverse asymptotic boundary. He is aiming to prove that these planes are also disjoint. Such a result will have a very wide range of applications in geometric topology. PROBLEM 3: (Properly Embedded Least Area Planes in Hyperbolic 3-space) Dr. Coskunuzer is aiming to prove another ambitious conjecture about the least area planes in hyperbolic 3-space in this project. The conjecture is that any least area plane in hyperbolic 3-space whose asymptotic boundary is a simple closed curve is properly embedded. He already got very strong partial results about the conjecture. PROBLEM 4: (Hyperbolic 3-manifolds with Minimal Foliation) The next problem in the project is the existence of a hyperbolic 3-manifold with foliation by minimal surfaces. This is also a famous question in geometric topology. PROBLEM 5: (Embedded Plateau Problem) The aim is to prove the following conjecture: For any nullhomotopic curve C in a 3-manifold M, there is an embedded disk which minimizes the area among the embedded disks in M with boundary C.
Оригинален текст от CORDIS (на английски).
Участници
- KOC UNIVERSITY · IstanbulКоординаторТурция
Връзки
Данни: CORDIS, © Европейски съюз