Article
Elliptic Weingarten surfaces: Singularities, rotational examples and the halfspace theorem
Author/s | Fernández Delgado, Isabel
![]() ![]() ![]() ![]() ![]() ![]() ![]() Mira Carrillo, Pablo |
Department | Universidad de Sevilla. Departamento de Matemática Aplicada I |
Publication Date | 2023 |
Deposit Date | 2023-04-12 |
Published in |
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Abstract | We 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 ... We 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 ellipsoids |
Funding agencies | Ministerio de Ciencia e Innovación (MICIN). España |
Project ID. | PID2020-118137GB-I00
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Citation | Fernández 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. |
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