In this paper, we study the Gauss map of a free boundary minimal surface. The main theorem asserts that if components are eigenfunctions Jacobi-Steklov operator, then surface must be rotationally symmetric.

For 0 ≤ α ≤ 1 given, we consider the α-continued fraction expansion of a real number obtained by iterating the map Aα(x) = ̨̨ x − ˆ x + 1− α ̃ ̨̨ defined on the interval Iα = (0, ᾱ), with ᾱ = max(α, 1− α). These maps generalize the classical (Gauss) continued fraction map which corresponds to the choice α = 1, and include the nearest integer (α = 1/2) and byexcess (α = 0) continued fraction expansio...

We propose a general paradigm for generating optimal coordinate frame fields that may be exploited to annotate and display curves and surfaces. Parallel-transport framings, which work well for open curves, generally fail to have desirable properties for cyclic curves and for surfaces. We suggest that minimal quaternion measure provides an appropriate generalization of parallel transport. Our fu...