PreprintarXiv licencearXiv
Embedded minimal surfaces with three ends associated with the Hoffman-Osserman catenoids
Abstract
For every positive integer g and every Hoffman-Osserman catenoid in ℝ5, we construct a complete embedded minimal surface of genus g that is not contained in any proper affine subspace of ℝ5. These surfaces can be viewed as higher-codimensional analogues of the Costa-Hoffman-Meeks surfaces, associated with the union of the corresponding Hoffman-Osserman catenoid and the plane containing its waist circle. We provide explicit Weierstrass data for these surfaces. Our construction can also be interpreted as restoring conformality to a deformed Costa-Hoffman-Meeks immersion by introducing two additional harmonic coordinate functions.
Related
- Minimal surfaces in ℍ2×ℝ with finite total curvature and embedded ends
- Uniqueness of embedded minimal Lagrangian tori in ℂℙ2
- Existence of rotationally symmetric embedded f-minimal tori
- Properly embedded Legendrian surfaces in the tangent sphere bundle of hyperbolic space
- The Smoothability of Embedded Surfaces in 4-Manifolds Under Stabilizations
BibTeX
@misc{lee2026embedded,
title = {{Embedded minimal surfaces with three ends associated with the Hoffman-Osserman catenoids}},
author = {Jaehoon Lee and Eungbeom Yeon},
howpublished = {arXiv},
year = {2026},
month = oct,
doi = {10.48550/arxiv.2610.34856},
eprint = {2610.34856},
archivePrefix = {arXiv},
url = {https://arxiv.org/abs/2610.34856},
}
RIS
TY - UNPB
TI - Embedded minimal surfaces with three ends associated with the Hoffman-Osserman catenoids
AU - Jaehoon Lee
AU - Eungbeom Yeon
PY - 2026
DA - 2026/10/26
PB - arXiv
DO - 10.48550/arxiv.2610.34856
UR - https://arxiv.org/abs/2610.34856
AB - For every positive integer g and every Hoffman-Osserman catenoid in ℝ^5, we construct a complete embedded minimal surface of genus g that is not contained in any proper affine subspace of ℝ^5. These surfaces can be viewed as higher-codimensional analogues of the Costa-Hoffman-Meeks surfaces, associated with the union of the corresponding Hoffman-Osserman catenoid and the plane containing its waist circle. We provide explicit Weierstrass data for these surfaces. Our construction can also be interpreted as restoring conformality to a deformed Costa-Hoffman-Meeks immersion by introducing two additional harmonic coordinate functions.
ER -