Year: 2026
Type: paratext
Abstract: We classify complete, two-sided, properly embedded capillary minimal surfaces with nonempty boundary and Morse index one in \(\mathbb R^3_+\). More precisely, if the boundary is compact, these surfaces are catenoid truncations; if the boundary is noncompact, they are capillary hairpin surfaces. The classification extends to higher dimensions under extrinsic Euclidean volume growth and Wang--Zhang's dimension and angle conditions.
Source: arXiv (Cornell University)
Author: Lu, Chenghang
Language: English
Subfield: Applied Mathematics
Field: Mathematics
Domain: Physical Sciences
Open Access status: green
OpenAlex ID: W7223067988