Asymptotic behavior of flows by powers of the Gaussian curvature
Montag, 13.5.19, 16:00-17:00, Raum 125, Ernst-Zermelo-Str. 1
In this talk, I will introduce the ideas of\nBrendle-Choi-Daskaspoulos' paper "Asymptotic behavior of flows by powers of the Gaussian curvature".\nAnd I will try to use their idea to treat some other similar problems and show where the difficulities are.
Q-Curvature Equation in Dimension 1
Dienstag, 25.6.19, 16:00-17:00, Raum 404, Ernst-Zermelo-Str. 1
Stability of graph tori with almost nonnegative scalar curvature
Dienstag, 2.7.19, 16:00-17:00, Raum 404, Ernst-Zermelo-Str. 1
Interior estimate for scalar curvature equations
Dienstag, 16.7.19, 16:00-17:00, Raum 404, Ernst-Zermelo-Str. 1
Motivated by the isometric embedding problem and fully\nnonlinear PDE theory, we study the apriori estimate for scalar curvature equations. Joint with Prof. Pengfei Guan, we proved that there is an interior second order estimate for isometrically embedded hypersurfaces with positive scalar curvature. By employing Warren and Yuan's integral method and my new observation in three-dimensional hypersurface with positive scalar curvature, I give an affirmatively answer to the interior second order estimate to this fully nonlinear PDE in dimension three.
Maximum principles for a fully nonlinear nonlocal equation on unbounded domains
Dienstag, 23.7.19, 16:00-17:00, Raum 404, Ernst-Zermelo-Str. 1