Event
01_1
| 제출번호(No.) | 0087 |
|---|---|
| 분류(Section) | Invited Talk |
| 분과(Session) | Analysis (AN) |
| 영문제목 (Title(Eng.)) |
The threshold theorem for the hyperbolic Yang-Mills equation |
| 저자(Author(s)) |
Sung-Jin Oh1, Daniel Tataru2 KIAS1, UC Berkeley2 |
| 초록본문(Abstract) | In this talk, I will present the recent proof of the Threshold Theorem for the energy critical hyperbolic Yang-Mills equation in (4+1) dimensions. In particular, we give sharp criteria for global existence and scattering in terms of the energy of the initial data, as well as in terms of bubbling-off a harmonic Yang-Mills connection. Our proof lies at the intersection of many recent developments, including null form estimates and function spaces; parametrix construction via gauge renormalization; induction on energy; monotonicity formulae arising from the normalized scaling vector field etc. Also of note is the use of the associated parabolic flow, namely the Yang-Mills heat flow, to construct a high quality global gauge (called the caloric gauge), extending the idea of Tao for the harmonic map heat flow. [This is a joint work with D. Tataru (UC Berkeley)] |
| 분류기호 (MSC number(s)) |
70S15, 35L71 |
| 키워드(Keyword(s)) | Yang-Mills, threshold theorem, bubbling, caloric gauge |
| 강연 형태 (Language of Session (Talk)) |
English |