TITLE:
NUVO Space II: Analysis and Variational Structure on NUVO Space
AUTHORS:
Rickey W. Austin
KEYWORDS:
NUVO Manifold, Conformal Laplacian, Bochner Identity, Weighted Sobolev Spaces, Scalar Field Dynamics, Conformal Variational Geometry
JOURNAL NAME:
Journal of Applied Mathematics and Physics,
Vol.13 No.11,
November
3,
2025
ABSTRACT: We develop the analytic, geometric, and variational framework on NUVO space, the conformally flat manifold
(
M,g
)
with
g=
λ
2
η
introduced in Part I. Weighted divergence and Stokes theorems, curvature identities, and the Laplace-Beltrami operator are derived in full detail. We construct the variational principles governing geodesic motion and scalar currents and prove the existence and regularity of solutions to representative nonlinear scalar field equations. Together with Part I, this paper provides the mathematical foundation required for subsequent applications to gravitation and field dynamics.