The Gauss map of a free boundary minimal surface
Hung Tran
TL;DR
This paper investigates the Gauss map of free boundary minimal surfaces and establishes that if certain components are eigenfunctions of the Jacobi-Steklov operator, then the surface exhibits rotational symmetry.
Contribution
It introduces a new characterization linking the eigenfunctions of the Jacobi-Steklov operator to rotational symmetry in free boundary minimal surfaces.
Findings
Components of the Gauss map as eigenfunctions imply rotational symmetry.
Provides a new criterion for symmetry based on spectral properties.
Enhances understanding of the geometric structure of free boundary minimal surfaces.
Abstract
In this paper, we study the Gauss map of a free boundary minimal surface. The main theorem asserts that if components of the Gauss map are eigenfunctions of the Jacobi-Steklov operator, then the surface must be rotationally symmetric.
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