报告题目：The Asymptotic Plateau Problem for $p$-Convex Hypersurfaces in Hyperbolic Space

报 告 人：隋哲楠 副教授（哈尔滨工业大学）

报告时间：2026年10月22日（星期四）1500—16:00

报告地点：数学科学学院114（小报告厅）

校内联系人：王国栋 副教授   联系方式：84708351-8503

报告摘要：We solve the asymptotic Plateau problem in hyperbolic space for the curvature given by the normalized geometric mean of the $p$-fold sums of the principal curvatures. For every $n\ge3$, $2\le p\le n-1$, and $\sigma\in(0,1)$, each bounded domain $\Omega\subset\mathbb{R}^n$ with smooth mean-convex boundary admits a unique complete admissible vertical graph with prescribed curvature $\sigma$ and asymptotic boundary $\partial\Omega\times\{0\}$. The result extends the known cases $(n,p)=(3,2)$ and $(4,3)$ to the stated range. The key curvature estimate is uniform with respect to the positive boundary height in the approximating Dirichlet problems. The proof establishes two lower bounds for the full third-derivative quadratic form under the linearized constraints: a sharp universal bound with coefficient $2/p$ and a stronger direction-dependent bound when the relevant principal curvature lies in a specified range. This is joint work with Shujun Shi.

报告人简介：哈尔滨工业大学副教授，2015年博士毕业于俄亥俄州立大学，研究方向为几何分析，具体包括完全非线性方程的先验估计和预定曲率与超曲面问题等，在Analysis & PDE, CPDE, JFA,IMRN等期刊发表论文十余篇。