YPERVOLIKĪ ANALYSĪ KAI GEŌMETRIA
| Title | ΥΠΕΡΒΟΛΙΚΗ ΑΝΑΛΥΣΗ ΚΑΙ ΓΕΩΜΕΤΡΙΑ / YPERVOLIKĪ ANALYSĪ KAI GEŌMETRIA |
| Code | Θ021 |
| Faculty | Sciences |
| School | Mathematics |
| Cycle / Level | 2nd / Postgraduate |
| Teaching Period | Winter/Spring |
| Coordinator | Anestis Fotiadis |
| Common | No |
| Status | Active |
| Course ID | 600025910 |
Programme of Study: PMS Tmīmatos Mathīmatikṓn (2025-2030)
Registered students: 0
| Orientation | Attendance Type | Semester | Year | ECTS |
|---|---|---|---|---|
| THEŌRĪTIKA MATHĪMATIKA | Elective Courses belonging to the selected specialization | Winter | - | 10 |
| Academic Year | 2025 – 2026 |
| Class Period | Winter |
| Faculty Instructors | |
| Weekly Hours | 3 |
| Total Hours | 39 |
| Class ID | 600268386
|
Mode of Delivery
- Face to face
- Distance learning
Digital Course Content
- e-Study Guide https://qa.auth.gr/en/class/1/600268386
Erasmus
The course is also offered to exchange programme students.
General Competences
- Advance free, creative and causative thinking
Course Content (Syllabus)
Mobius transformation, basic models of hyperbolic geometry, isometries, hyperbolic distance function, comparison with Euclidean geometry, groups of isometries, fundamental domains, limit set, hyperbolic surfaces, heat kernel estimates
Keywords
Hyperbolic space, group of isometries, limit points, hyperbolic surfaces, heat kernel
Educational Material Types
- Notes
Course Organization
| Activities | Workload | ECTS | Individual | Teamwork | Erasmus |
|---|---|---|---|---|---|
| Lectures | 300 | ✓ | |||
| Total | 300 |
Bibliography
Additional bibliography for study
1. Davies E.B. and N. Mandouvalos (1988). Heat Kernel Bounds on Hyperbolic
Space and Kleinian Groups. Proc. London Math. Soc. 57 (No 3): 182-208.
2. Davies E.B. and N. Mandouvalos (1987). Heat Kernel Bounds on Manifolds
with Cusps. J. Funct. Anal. 75 (No 2): 311-322.
3. Mandouvalos N. (1988). Spectral Theory and Eisenstein Series for Kleinian
4. http://homepages.warwick.ac.uk/~masbb/Papers/MA448.pdf
Groups. Proc. London Math. Soc. 57 (No 3): 209-238.
4. Mandouvalos N. (1989). Scattering Operator, Eisenstein Series, Inner Product
Formula and “Maass-Selberg” relations for Kleinian Groups. Memoirs Amer.
Math. Soc. 400.
Last Update
11-09-2025
