Year: 2026
Type: preprint
Abstract: We prove that a complete, connected, two-sided, embedded free boundary minimal hypersurface of finite total curvature and Morse index one in a half-space of RN, with nonempty boundary is a higher-dimensional half-catenoid. We also prove that a complete, connected, two-sided, embedded free boundary minimal hypersurface of finite total curvature and Morse index one in a quarter-space is the higher-dimensional quarter-catenoid.
Source: arXiv (Cornell University)
Author: Li, Junzhang
Language: English
Subfield: Applied Mathematics
Field: Mathematics
Domain: Physical Sciences
Open Access status: green
OpenAlex ID: W7223197524