arXiv subjects
Publications and source records attributed to José L. Teruel.
In this paper, we study oriented surfaces S in $\mathbb{R}^3$, called Surfaces with quadratic support function of harmonic type (in short HQSF-surfaces), these surfaces generalize the QSF-surfaces. We obtain a Weierstrass type representation for the HQSF-surfaces which depends on three holomorphic functions. Moreover, we classify the HQSF-surfaces of rotation.
In this paper we extend Efimov's Theorem by proving that any complete surface in $\mathbb{R}^3$ with Gauss curvature bounded above by a negative constant outside a compact set has finite total curvature, finite area and is properly immersed. Moreover, its ends must be asymptotic to half-lines. We also give a partial solution to Milnor's conjecture by studying isometric immersions in a space form of complete surfaces which satisfy that outside a compact set they have non positive Gauss curvature and the square of a principal curvature function is bounded from below by a positive constant.