Monge-Ampère Equations Determining Optimal Dyson Shell Curvature via Perfectoid Modular Forms
Year: 2025
Type: article
Abstract: Mathematical Applications of Science Fiction We present a rigorous derivation of the optimal curva-ture tensor for a Dyson Shell megastructure enclosing aG-type main-sequence star. By modeling the shell as a com-pact Kähler manifold X embedded in a non-Archimedeanprojective space, we reduce the structural stability prob-lem to a complex Monge-Ampère equation of the form(ω + i∂ ¯∂φ)n = eF ωn. We introduce a novel class of motivicL-functions to regularize the stress-energy tensor at thepoles, utilizing the theory of perfectoid spaces to handlethe infinite-dimensional moduli space of shell perturbations.We prove the existence and uniqueness of a canonical metricthat minimizes the Hilbert-Schmidt norm of the Ricci cur-vature, thereby maximizing the structural integrity againstgravitational shear. The proof relies on a modified continu-ity method involving C2,α a priori estimates and a vanishingtheorem for the first Chern class of the structural sheaf.
Authors: Revista, Zen, MFC, 10
Language: English
Subfield: Geometry and Topology
Field: Mathematics
Domain: Physical Sciences
Open Access status: green
OpenAlex ID: W7117894641
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