Informace o publikaci
The Dirichlet-to-Neumann map for Poincaré–Einstein fillings
| Autoři | |
|---|---|
| Rok publikování | 2026 |
| Druh | Recenzovaný odborný článek |
| Časopis / Zdroj | REVISTA MATEMATICA IBEROAMERICANA |
| Fakulta / Pracoviště MU | |
| Citace | |
| www | https://ems.press/journals/rmi/articles/14299243 |
| Doi | https://doi.org/10.4171/rmi/1586 |
| Klíčová slova | conformal geometry; Poincaré–Einstein manifolds; Dirichlet-to-Neumann map; renormalized volume |
| Přiložené soubory | |
| Popis | We study the non-linear Dirichlet-to-Neumann map for the Poincaré–Einstein filling problem. For even-dimensional manifolds, the range of this non-local map is described in terms of a rank-two “Dirichlet-to-Neumann tensor” along the boundary determined by the Poincaré–Einstein metric. This tensor is proportional to the variation of renormalized volume along a path of Poincaré–Einstein metrics. We construct natural “Dirichlet-to-Neumann hypersurface invariants” that are conformally invariant and recover all Dirichlet-to-Neumann tensors. We give an explicit formula for these hypersurface invariants and use a new vanishing result for odd order T-curvatures to show that they are the unique, natural conformal hypersurface invariant of transverse order equalling the boundary dimension. We also construct such conformally invariant Dirichlet-to-Neumann hypersurface invariants for Poincaré–Einstein fillings for odd-dimensional manifolds with conformally flat boundary. |
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