2023-04-122023-04-122023Fernández Delgado, I. y Mira Carrillo, P. (2023). Elliptic Weingarten surfaces: Singularities, rotational examples and the halfspace theorem. Nonlinear Analysis, 232. https://doi.org/10.1016/j.na.2023.113244.0362-546X (impreso)1873-5215 (online)https://hdl.handle.net/11441/144242We show by phase space analysis that there are exactly 17 possible qualitative behaviors for a rotational surface in R3 that satisfies an arbitrary elliptic Weingarten equation W(κ1, κ2) = 0, and study the singularities of such examples. As global applications of this classification, we prove a sharp halfspace theorem for general elliptic Weingarten equations of finite order, and a classification of peaked elliptic Weingarten ovaloids with at most 2 singularities. In the case that W is not elliptic, we give a negative answer to a question by Yau regarding the uniqueness of rotational ellipsoidsapplication/pdf27engAttribution-NonCommercial-NoDerivatives 4.0 Internacionalhttp://creativecommons.org/licenses/by-nc-nd/4.0/Weingarten surfacesFully nonlinear elliptic equationsPhase space analysisHalfspace theoremIsolated singularitiesRotational surfacesinfo:eu-repo/semantics/articleinfo:eu-repo/semantics/openAccess10.1016/j.na.2023.113244