PDE Real Analysis Seminar

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Date, time & place Tuesday 10:30 - 11:30 056Room #056 (Graduate School of Math. Sci. Bldg.)

2016/10/11

10:30-11:30   Room #056 (Graduate School of Math. Sci. Bldg.)
Nam Quang Le (Indiana University)
Global solutions to the second boundary value problem of the prescribed affine mean curvature and Abreu's equations (English)
[ Abstract ]
The second boundary value problem of the prescribed affine mean curvature equation is a nonlinear, fourth order, geometric partial differential equation. It was introduced by Trudinger and Wang in 2005 in their investigation of the affine Plateau problem in affine geometry. The previous works of Trudinger-Wang, Chau-Weinkove and the author solved this global problem under some restrictions on the sign or integrability of the affine mean curvature. In this talk, we explain how to remove these restrictions and obtain global solutions under optimal integrability conditions on the affine mean curvature. Our analysis also covers the case of Abreu's equation arising in complex geometry.