Elliptic Weingarten surfaces: Singularities, rotational examples and the halfspace theorem
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 shar...
| Autores: | , |
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| Tipo de recurso: | artículo |
| Estado: | Versión publicada |
| Fecha de publicación: | 2023 |
| País: | España |
| Institución: | Universidad de Sevilla (US) |
| Repositorio: | idUS. Depósito de Investigación de la Universidad de Sevilla |
| OAI Identifier: | oai:idus.us.es:11441/144242 |
| Acceso en línea: | https://hdl.handle.net/11441/144242 https://doi.org/10.1016/j.na.2023.113244 |
| Access Level: | acceso abierto |
| Palabra clave: | Weingarten surfaces Fully nonlinear elliptic equations Phase space analysis Halfspace theorem Isolated singularities Rotational surfaces |
| Sumario: | 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 |
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