Abstract: We introduce a method of constructing (generalized) capillary surfaces via Gromov's "$\mu$-bubble" method. Using this, we study low-dimensional manifolds with nonnegative scalar curvature and strictly mean convex boundary. We prove a fill-in question of Gromov, a band-width estimate, and a compactness conjecture of M. Li in the case of surfaces.

Biography: Yujie Wu is currently a Ph.D. Student at Stanford University. Her research focused on geometric analysis and PDEs, in particular minimal surface theory and the Allen Cahn equation.

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