Abstract: In this talk, I will discuss isoperimetric inequalities for the first Steklov eigenvalue above the ground state in hyperbolic and spherical spaces, at frequencies naturally associated with free boundary minimal submanifolds in geodesic balls. We establish sharp volume comparisons and size-independent product inequalities. Under a perimeter constraint, we prove Weinstock-type inequalities for smooth bounded outward-minimizing domains in $\mathbb{H}^n$ and for convex domains in $\mathbb{S}^n_+$ under explicit radius conditions. We also obtain product inequalities for minimal submanifolds and reciprocal-sum estimates under a boundary moment condition. This is joint work with Pingxin Gu.

Brief biography: Yao Wan is currently a postdoctoral fellow at The Chinese University of Hong Kong under the mentorship of Prof. Martin Li. He obtained his Ph.D. from Tsinghua University in 2024 under the supervision of Prof. Haizhong Li. His research focuses on geometric analysis and convex geometry.

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