Abstract
Regularity properties of intrinsic objects for a large class of Stein Manifolds, namely of Monge–Ampère exhaustions and Kobayashi distance, is interpreted in terms of modular data. The results lead to a construction of an infinite dimensional family of convex domains with squared Kobayashi distance of prescribed regularity properties. A new sharp refinement of Stoll’s characterization of \(\mathbb {C}^{n}\) is also given.
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G. Patrizio and A. Spiro were partially supported by the Project MIUR “Real and Complex Manifolds: Geometry, Topology and Harmonic Analysis” and by GNSAGA of INdAM.
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Patrizio, G., Spiro, A. Modular data and regularity of Monge–Ampère exhaustions and of Kobayashi distance. Math. Ann. 362, 425–449 (2015). https://doi.org/10.1007/s00208-014-1124-5
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DOI: https://doi.org/10.1007/s00208-014-1124-5