H-principles for Holomorphic Partial Differential Relations
In this Thesis we introduce the notion of the realifications of an arbitrary Holomorphic Partial Differential Relation, i.e. a subset of a jet bundle of local holomorphic sections. Our main result states that if any realification of an open Holomorphic Partial Differential Relation over a Stein mani...
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| Tipo de recurso: | tesis doctoral |
| Fecha de publicación: | 2025 |
| País: | España |
| Institución: | Universidad Complutense de Madrid (UCM) |
| Repositorio: | Docta Complutense |
| Idioma: | inglés |
| OAI Identifier: | oai:docta.ucm.es:20.500.14352/115191 |
| Acceso en línea: | https://hdl.handle.net/20.500.14352/115191 |
| Access Level: | acceso abierto |
| Palabra clave: | 517.95(043.2) Derivadas Parciales Matemáticas (Matemáticas) 12 Matemáticas |
| Sumario: | In this Thesis we introduce the notion of the realifications of an arbitrary Holomorphic Partial Differential Relation, i.e. a subset of a jet bundle of local holomorphic sections. Our main result states that if any realification of an open Holomorphic Partial Differential Relation over a Stein manifold satisfies a relative to domain h–principle, then it is possible to deform any formal solution into one that is holonomic in a neighbourhood of a Lagrangian skeleton of the Stein manifold. If the Stein manifold is an open Riemann surface or it has finite type, then that skeleton is independent of the formal solution. This yields the existence of localh–principles over that skeleton. These results broaden those obtained by F. Forstneric and M. Slapar on holomorphic immersions, submersions and complex contact structures for instance to holomorphic local h–principles for complex even contact, holomorphic Engel or complex locally conformal symplectic structures... |
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