Characterization of Lipschitz normally embedded complex curves and Lipschitz trivial values of polynomial mappings
We study Lipschitz geometry of fibers of complex polynomial mappings from two points of view: the equivalence of inner and outer metrics of an algebraic curve and the existence of a locally bi-Lipschitz trivial fibre bundle structure over a subset of values of polynomial mappings. We prove that the...
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| Tipo de recurso: | tesis doctoral |
| Estado: | Versión publicada |
| Fecha de publicación: | 2023 |
| País: | Brasil |
| Institución: | Universidade Federal do Ceará (UFC) |
| Repositorio: | Repositório Institucional da Universidade Federal do Ceará (UFC) |
| Idioma: | inglés |
| OAI Identifier: | oai:repositorio.ufc.br:riufc/70235 |
| Acceso en línea: | http://www.repositorio.ufc.br/handle/riufc/70235 |
| Access Level: | acceso abierto |
| Palabra clave: | Geometria Lipschitz Lipschitz normalmente mergulhado Valores Lipschitz triviais Lipschitz geometry Lipschitz normally embedded Lipschitz trivial values |
| Sumario: | We study Lipschitz geometry of fibers of complex polynomial mappings from two points of view: the equivalence of inner and outer metrics of an algebraic curve and the existence of a locally bi-Lipschitz trivial fibre bundle structure over a subset of values of polynomial mappings. We prove that the affi ne part of a connected projective algebraic curve is Lipschitz normally embedded if and only if the following three conditions are satisfi ed: its affi ne part is connected, its affi ne part is locally Lipschitz normally embedded at each of its singular points; and its degree equals to the number of its points at infi nity. Moreover, we show that any Lipschitz trivial value of a real or complex polynomial mapping is a suspension of a regular value of properness of a polynomial mapping in fewer variables. Last, we show that this result cannot extend to rational mappings. |
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