國立清華大學 數學系

Title: Geometric PDE--some basic tools Lecture 1: Sobolev embedding, Moser-Trudinger inequality on domains (1/21) Lecture 2: Moser's inequality on $S^2$, Carleson-Chang existence theorem (1/22) Lecture 3: Onofri inequality, Uniformization Theorem on 2-surfaces (1/23) Lecture 4: GJMS operators, Q-curvature (1/28) Lecture 5: Positivity of Paneitz operators (1/29) Lecture 6: Fractional Laplacian operators (1/30) Abstract: We plan to cover some basic tools which are frequently used in elliptic PDE arising from problems in conformal geometry. The course assumes background in PDE and differential geometry at the undergraduate level. Time: 2013, Jan. 21, Jan. 22, Jan 23, Jan. 28, Jan 29, Jan. 30 Course: 10:30 - 12:00 (1/21, 1/22, 1/23, 1/28, 1/29, 1/30) Forum: 14:00 - 15:30 (1/30) Study Seminar: 14:00 - 15:30 (1/21, 1/22, 1/23, 1/28, 1/29)