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RCD(K,\infty) path spaces exhibit stability under singular Kato–Voigt perturbations via Mosco convergence, and their curvature shifts can be characterized through the Evolution Variational Inequality on Wasserstein space, linking geometric curvature bounds with spectral perturbations of the associated Dirichlet form. Novelty: ClaimNovelty.NOVEL_FINDING. Consensus alignment: ConsensusAlignment.NEUTRAL.

May 5, 2026Open Access

Rigidity and Stability of RCD (K, ) Path Spaces under Singular Kato–Voigt Perturbations

Key Points

The aim is to explore the rigidity and stability of RCD(K,∞) path spaces under singular perturbations.
Analysis using L^2-normed modules and Gigli’s differential calculus.
Closure of the Γ2-operator on ℝ²,² was established.
Stability was proven via Mosco convergence.
Characterized curvature shifts through the Evolution Variational Inequality (EVI) on Wasserstein space P₂(Ω).
Linked geometric curvature bounds with spectral perturbations of the associated Dirichlet form.

Abstract

We study the rigidity and stability properties of RCD (K, ) path spaces constructed over metric measure spaces via projective limits. The analysis is performed within the framework of L²-normed modules and Gigli’s differential calculus. We establish the closure of the ₂-operator on D^2, 2, identify the intrinsic Hessian as a Riesz representative, and prove stability under singular Kato–Voigt perturbations via Mosco convergence. The main rigidity result characterizes curvature shifts through the Evolution Variational Inequality (EVI) on Wasserstein space P₂ (), linking geometric curvature bounds with spectral perturbations of the associated Dirichlet form.

Rigidity and Stability of RCD (K, ) Path Spaces under Singular Kato–Voigt Perturbations

Key Points

Abstract

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