Jared Marx-Kuo (Rice University)

Title: Infinitely Many Surfaces with Prescribed Mean Curvature in the Presence of a Strictly Stable Minimal Surface

Abstract:  We construct infinitely many distinct hypersurfaces with prescribed mean curvature (PMC) for a large class of prescribing functions on closed manifolds, $(M^{n+1}, g)$, containing a strictly stable minimal surface. Such a strictly stable minimal surface exists when $H_n(M^{n+1)) \neq 0$ or if $(M^{n+1}, g)$ does not satisfy the Frankel property. Our construction synthesizes ideas from Song's construction of infinitely many minimal surfaces
in the non-generic setting, Dey's construction of multiple constant mean curvature surfaces, and Sun--Wang--Zhou's min-max construction of free boundary PMCs.