报告摘要： The stable Bernstein problem for minimal hypersurfaces asks whether a complete, two-sided, stable minimal hypersurface in $R^{n+1}$ is flat. This problem is a geometric generalization of the classical Bernstein problem for the minimal surface equation, and has played a key role in the application of minimal surfaces in Riemannian geometry. When $n=2$, the question was answered in the affirmative in 1979. I will discuss recent solutions of this problem when $n=3$. The proof relies on an intriguing relation between the stability condition and the geometry of positive scalar curvature. If time permits, I will also talk about an extension to anisotropic minimal hypersurfaces. This is based on joint work with Otis Chodosh.

个人简介：I am an assistant professor at Courant Institute of Mathematical Sciences, New York University. Previously, I was an instructor at Princeton University. I got my Ph.D. at Stanford University. My dissertation advisors are Rick Schoen and Brian White. Before that I was an undergraduate student at Peking University, where I got my Bachelor's degree in Mathematics, mentored by Huijun Fan.

My research interests include differential geometry, partial differential equations, and geometric measure theory. Specifically, my recent work concerns minimal surfaces, scalar curvature and mathematical general relativity.